Tariffazione con i GLM
Statistica Assicurativa
Leonardo Stincone, 10/02/2020
libname dati '/folders/myfolders/data';
ods graphics on / width = 10cm height = 8cm;
data polizze;
set dati.polizze;
run;
data polizze;
set polizze;
freqsin = nsin / espo;
run;
data polizze_sin;
set polizze;
where nsin > 0;
dannomedio = dannotot / nsin;
run;
proc print data = polizze (obs=10) round;
run;
SAS Connection established. Subprocess id is 2476
SAS Output
| F |
35 |
MI |
NO |
B |
18 |
620 |
10 |
1.0 |
0 |
0.00 |
0 |
| M |
37 |
AP |
NO |
B |
37 |
790 |
12 |
1.0 |
0 |
0.00 |
0 |
| M |
45 |
LE |
NO |
B |
63 |
850 |
15 |
1.0 |
0 |
0.00 |
0 |
| F |
21 |
PS |
NO |
B |
34 |
710 |
13 |
1.0 |
0 |
0.00 |
0 |
| M |
48 |
SP |
NO |
B |
33 |
770 |
12 |
0.2 |
0 |
0.00 |
0 |
| F |
45 |
TO |
NO |
B |
44 |
780 |
14 |
1.0 |
0 |
0.00 |
0 |
| M |
35 |
PG |
NO |
D |
51 |
1035 |
19 |
1.0 |
0 |
0.00 |
0 |
| M |
70 |
PG |
SI |
B |
65 |
970 |
15 |
1.0 |
0 |
0.00 |
0 |
| F |
46 |
AR |
NO |
B |
61 |
820 |
15 |
1.0 |
0 |
0.00 |
0 |
| M |
55 |
AR |
NO |
B |
80 |
1180 |
18 |
1.0 |
1 |
359.06 |
1 |
1) Analisi preliminari
proc means data = polizze nway noprint;
var espo nsin dannotot;
output out = polizzeMeans sum = totespo totnsin totdannotot;
run;
data polizzeMeans;
set polizzeMeans;
totfreqsin = totnsin / totespo;
if totnsin > 0 then totdannomed = totdannotot / totnsin;
else totdannomed=0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
format totfreqsin 5.3;
format totespo 10.2;
format totdannotot 10.2;
format totqd 10.2;
run;
proc print data = polizzeMeans noobs round;
var totfreqsin totdannomed totqd totespo;
run;
SAS Output
| 0.103 |
3000 |
308.83 |
123282.32 |
proc means data = polizze maxdec = 2;
var eta potf potkil massa;
weight espo;
run;
SAS Output
|
|
|
172161
172161
172161
172161
|
|
|
|
95.00
41.00
362.00
2240.00
|
1. Sesso
proc means data = polizze nway noprint;
class sesso;
var espo nsin dannotot;
output out = polizzebysesso sum = totespo totnsin totdannotot;
run;
data polizzebysesso;
set polizzebysesso;
totfreqsin = totnsin / totespo;
if totnsin > 0 then totdannomed = totdannotot / totnsin;
else totdannomed=0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
format totfreqsin 5.3;
format totespo 10.2;
format totdannotot 10.2;
format totqd 10.2;
run;
proc print data = polizzebysesso noobs;
var sesso totfreqsin totdannomed totqd totespo;
run;
SAS Output
| F |
0.098 |
2758.37 |
269.97 |
39735.73 |
| M |
0.105 |
3106.76 |
327.31 |
83546.59 |
proc sgplot data=polizze;
vline sesso / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05;
run;
SAS Output
proc sgplot data=polizze_sin;
vline sesso / response=dannomedio weight=nsin stat=mean limitstat=clm alpha = .05;
run;
SAS Output
2. Capoluogo
proc means data = polizze nway noprint;
class capoluogo;
var espo nsin dannotot;
output out = polizzebycapoluogo sum = totespo totnsin totdannotot;
run;
data polizzebycapoluogo;
set polizzebycapoluogo;
totfreqsin = totnsin / totespo;
if totnsin > 0 then totdannomed = totdannotot / totnsin;
else totdannomed=0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
format totfreqsin 5.3;
format totespo 10.2;
format totdannotot 10.2;
format totqd 10.2;
run;
proc print data=polizzebycapoluogo noobs;
var capoluogo totfreqsin totdannomed totqd totespo;
run;
SAS Output
| NO |
0.097 |
3117.84 |
301.35 |
101269.74 |
| SI |
0.132 |
2602.67 |
343.24 |
22012.58 |
proc sgplot data=polizze;
vline capoluogo / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05;
run;
SAS Output
proc sgplot data=polizze_sin;
vline capoluogo / response=dannomedio weight=nsin stat=mean limitstat=clm alpha = .05;
run;
SAS Output
3. Bendie
proc means data = polizze nway noprint;
class bendie;
var espo nsin dannotot;
output out=polizzebybendie sum=totespo totnsin totdannotot;
run;
data polizzebybendie;
set polizzebybendie;
totfreqsin = totnsin / totespo;
if totnsin > 0 then totdannomed = totdannotot / totnsin;
else totdannomed=0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
format totfreqsin 5.3;
format totespo 10.2;
format totdannotot 10.2;
format totqd 10.2;
run;
proc print data = polizzebybendie noobs;
var bendie totfreqsin totdannomed totqd totespo;
run;
SAS Output
| B |
0.099 |
3044.79 |
300.60 |
114456.64 |
| D |
0.158 |
2636.14 |
415.48 |
8825.68 |
proc sgplot data=polizze;
vline bendie / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05;
run;
SAS Output
proc sgplot data=polizze_sin;
vline bendie / response=dannomedio weight=nsin stat=mean limitstat=clm alpha = .05;
run;
SAS Output
4. Prov
proc means data = polizze nway noprint;
class prov;
var espo nsin dannotot;
output out = polizzebyprov sum = totespo totnsin totdannotot;
run;
data polizzebyprov;
set polizzebyprov;
totfreqsin = totnsin / totespo;
if totnsin > 0 then totdannomed = totdannotot / totnsin;
else totdannomed=0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
format totfreqsin 5.3;
format totespo 10.2;
format totdannotot 10.2;
format totqd 10.2;
run;
proc sort data = polizzebyprov;
by descending totfreqsin;
run;
proc print data = polizzebyprov (obs = 10);
var prov totfreqsin totdannomed totqd totespo;
run;
SAS Output
| KR |
0.247 |
3052.88 |
753.71 |
8.10 |
| NA |
0.166 |
2255.60 |
374.41 |
2138.67 |
| AO |
0.165 |
1607.49 |
265.26 |
145.44 |
| CE |
0.162 |
1999.70 |
323.63 |
1211.09 |
| ROMA |
0.146 |
2239.97 |
326.51 |
617.43 |
| CA |
0.145 |
2485.66 |
359.45 |
567.04 |
| SP |
0.142 |
3161.38 |
449.80 |
611.48 |
| PT |
0.142 |
3019.11 |
427.32 |
847.82 |
| TA |
0.141 |
1735.74 |
244.96 |
524.35 |
| PA |
0.140 |
2130.07 |
298.28 |
692.70 |
ods graphics on / width = 16cm height = 10cm;
proc sgplot data=polizze;
vline prov / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05
categoryorder=respdesc;
yaxis min = 0.05 max = 0.25;
run;
SAS Output
5. eta
proc means data = polizze nway noprint;
class eta;
var espo nsin dannotot;
output out = polizzebyeta sum = totespo totnsin totdannotot;
run;
data polizzebyeta;
set polizzebyeta;
totfreqsin = totnsin / totespo;
if totnsin > 0 then totdannomed = totdannotot / totnsin;
else totdannomed=0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
format totfreqsin 5.3;
format totespo 10.2;
format totdannotot 10.2;
format totqd 10.2;
run;
proc print data = polizzebyeta (obs=10) noobs;
var eta totfreqsin totdannomed totqd totespo;
run;
SAS Output
| 18 |
0.253 |
2816.35 |
711.71 |
91.01 |
| 19 |
0.190 |
6995.11 |
1332.43 |
593.24 |
| 20 |
0.208 |
3387.97 |
703.64 |
1266.33 |
| 21 |
0.158 |
3988.27 |
629.14 |
1939.81 |
| 22 |
0.174 |
2767.00 |
482.41 |
2156.65 |
| 23 |
0.141 |
4512.06 |
636.44 |
2566.41 |
| 24 |
0.144 |
2912.02 |
417.98 |
2724.07 |
| 25 |
0.129 |
3168.98 |
408.31 |
2832.83 |
| 26 |
0.129 |
3389.06 |
437.45 |
2974.93 |
| 27 |
0.108 |
2897.50 |
313.58 |
3132.37 |
proc sgplot data=polizze;
vline eta / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05;
yaxis min = 0.05 max = 0.30;
run;
SAS Output
proc sgplot data=polizze_sin;
vline eta / response=dannomedio weight=nsin stat=mean limitstat=clm alpha = .05;
yaxis min = 0 max = 8000;
run;
SAS Output
2) Cluster Analysis
2.1. Prov
proc cluster method = ward data = polizzebyprov outtree = clusterprov print = 5;
id prov;
var totfreqsin;
freq totespo;
copy totespo totnsin totdannotot totdannomed;
run;
SAS Output
The CLUSTER Procedure
Ward's Minimum Variance Cluster Analysis
| CL16 |
CL10 |
9515 |
0.0285 |
.917 |
|
| CL11 |
CL8 |
52015 |
0.0528 |
.864 |
|
| CL6 |
CL7 |
61702 |
0.0656 |
.798 |
|
| CL5 |
CL4 |
61530 |
0.2080 |
.590 |
|
| CL2 |
CL3 |
123232 |
0.5902 |
.000 |
|
proc print data = clusterprov (obs = 10);
run;
SAS Output
| RSM |
|
103 |
0 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.000 |
0 |
0 |
RSM |
0.04 |
0 |
0.00 |
0.00 |
| VT |
CL102 |
103 |
944 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.090 |
0 |
0 |
VT |
944.67 |
85 |
157469.91 |
1852.59 |
| RC |
CL102 |
103 |
355 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.090 |
0 |
0 |
RC |
355.66 |
32 |
68799.84 |
2150.00 |
| BN |
CL101 |
103 |
60 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.132 |
0 |
0 |
BN |
60.39 |
8 |
13033.78 |
1629.22 |
| PO |
CL101 |
103 |
67 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.132 |
0 |
0 |
PO |
67.96 |
9 |
24085.55 |
2676.17 |
| OR |
CL100 |
103 |
186 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.091 |
0 |
0 |
OR |
186.91 |
17 |
156203.33 |
9188.43 |
| CN |
CL100 |
103 |
1154 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.091 |
0 |
0 |
CN |
1154.79 |
105 |
277702.80 |
2644.79 |
| VC |
CL99 |
103 |
1644 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.094 |
0 |
0 |
VC |
1644.71 |
154 |
295996.92 |
1922.06 |
| RA |
CL99 |
103 |
1303 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.094 |
0 |
0 |
RA |
1303.27 |
122 |
692249.43 |
5674.18 |
| EN |
CL98 |
103 |
124 |
0 |
0 |
0 |
1 |
. |
. |
. |
. |
. |
. |
0.097 |
0 |
0 |
EN |
124.29 |
12 |
15241.08 |
1270.09 |
Con 12 cluster arrivo a $R^2 ≥ 0.99$
proc tree data = clusterprov nclusters = 12 out = prov12cl noprint;
id prov;
copy totespo totnsin totdannotot totfreqsin totdannomed;
run;
data prov12cl;
set prov12cl;
if prov='RSM' then cluster=12;
run;
proc print data = prov12cl (obs = 10);
run;
SAS Output
| RSM |
0.04 |
0 |
0.00 |
0.000 |
0.00 |
12 |
|
| VT |
944.67 |
85 |
157469.91 |
0.090 |
1852.59 |
1 |
CL14 |
| RC |
355.66 |
32 |
68799.84 |
0.090 |
2150.00 |
1 |
CL14 |
| BN |
60.39 |
8 |
13033.78 |
0.132 |
1629.22 |
2 |
CL26 |
| PO |
67.96 |
9 |
24085.55 |
0.132 |
2676.17 |
2 |
CL26 |
| OR |
186.91 |
17 |
156203.33 |
0.091 |
9188.43 |
1 |
CL14 |
| CN |
1154.79 |
105 |
277702.80 |
0.091 |
2644.79 |
1 |
CL14 |
| VC |
1644.71 |
154 |
295996.92 |
0.094 |
1922.06 |
1 |
CL14 |
| RA |
1303.27 |
122 |
692249.43 |
0.094 |
5674.18 |
1 |
CL14 |
| EN |
124.29 |
12 |
15241.08 |
0.097 |
1270.09 |
3 |
CL20 |
proc means data = prov12cl nway noprint;
class cluster;
var totespo totnsin totdannotot;
output out = polizzebyclusterprov sum = totespocl totnsincl totdannototcl;
run;
data polizzebyclusterprov;
set polizzebyclusterprov;
totfreqsincl = totnsincl / totespocl;
if totnsincl > 0 then totdannomedcl = totdannototcl / totnsincl;
else totdannomedcl = 0;
totqdcl = totdannototcl / totespocl;
drop _type_;
rename _FREQ_ = numprov;
format totfreqsincl 5.3;
format totespocl 10.2;
format totdannototcl 10.2;
format totqdcl 10.2;
run;
proc print data = polizzebyclusterprov;
run;
SAS Output
| 1 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| 2 |
4 |
2158.09 |
289 |
537774.02 |
0.134 |
1860.81 |
249.19 |
| 3 |
12 |
12480.92 |
1215 |
3369680.21 |
0.097 |
2773.40 |
269.99 |
| 4 |
10 |
18644.35 |
1567 |
5068192.03 |
0.084 |
3234.33 |
271.84 |
| 5 |
15 |
15491.65 |
1603 |
5149935.33 |
0.103 |
3212.69 |
332.43 |
| 6 |
9 |
12556.48 |
1378 |
4973336.43 |
0.110 |
3609.10 |
396.08 |
| 7 |
7 |
6464.18 |
758 |
2128488.68 |
0.117 |
2808.03 |
329.27 |
| 8 |
6 |
17521.58 |
2133 |
5941180.86 |
0.122 |
2785.36 |
339.08 |
| 9 |
6 |
3860.83 |
550 |
1377816.14 |
0.142 |
2505.12 |
356.87 |
| 10 |
8 |
7454.64 |
540 |
1906127.50 |
0.072 |
3529.87 |
255.70 |
| 11 |
4 |
3503.31 |
577 |
1237363.06 |
0.165 |
2144.48 |
353.20 |
| 12 |
4 |
1415.91 |
79 |
401864.78 |
0.056 |
5086.90 |
283.82 |
proc sort data = prov12cl;
by cluster;
run;
data prov12cl;
merge prov12cl polizzebyclusterprov;
by cluster;
run;
proc print data = prov12cl (obs = 10);
run;
SAS Output
| VT |
944.67 |
85 |
157469.91 |
0.090 |
1852.59 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| RC |
355.66 |
32 |
68799.84 |
0.090 |
2150.00 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| OR |
186.91 |
17 |
156203.33 |
0.091 |
9188.43 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| CN |
1154.79 |
105 |
277702.80 |
0.091 |
2644.79 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| VC |
1644.71 |
154 |
295996.92 |
0.094 |
1922.06 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| RA |
1303.27 |
122 |
692249.43 |
0.094 |
5674.18 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| LC |
119.11 |
11 |
24287.52 |
0.092 |
2207.96 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| FE |
964.48 |
89 |
207535.55 |
0.092 |
2331.86 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| SS |
531.54 |
47 |
169022.57 |
0.088 |
3596.22 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
| VV |
11.36 |
1 |
1580.75 |
0.088 |
1580.75 |
1 |
CL14 |
19 |
21730.39 |
2002 |
5981240.95 |
0.092 |
2987.63 |
275.25 |
proc sgplot data = prov12cl;
scatter x = totfreqsin y = totdannomed / group = cluster markerattrs=(symbol=CircleFilled);
run;
SAS Output
2.2. eta
proc means data = polizze nway noprint;
class eta;
var espo nsin dannotot;
output out = polizzebyeta sum = totespo totnsin totdannotot;
run;
data polizzebyeta;
set polizzebyeta;
totfreqsin = totnsin/totespo;
if totnsin>0 then totdannomed = totdannotot/totnsin;
else totdannomed = 0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
run;
proc print data = polizzebyeta (obs = 10) noobs;
var eta totfreqsin totdannomed totqd totespo;
run;
SAS Output
| 18 |
0.25271 |
2816.35 |
711.71 |
91.01 |
| 19 |
0.19048 |
6995.11 |
1332.43 |
593.24 |
| 20 |
0.20769 |
3387.97 |
703.64 |
1266.33 |
| 21 |
0.15775 |
3988.27 |
629.14 |
1939.81 |
| 22 |
0.17434 |
2767.00 |
482.41 |
2156.65 |
| 23 |
0.14105 |
4512.06 |
636.44 |
2566.41 |
| 24 |
0.14353 |
2912.02 |
417.98 |
2724.07 |
| 25 |
0.12885 |
3168.98 |
408.31 |
2832.83 |
| 26 |
0.12908 |
3389.06 |
437.45 |
2974.93 |
| 27 |
0.10822 |
2897.50 |
313.58 |
3132.37 |
proc sgplot data = polizzebyeta;
scatter x = eta y = totfreqsin / markerattrs=(symbol=CircleFilled);
series x = eta y = totfreqsin;
run;
SAS Output
proc format;
value formateta
low-22 = "18-22"
23-24 = "23-24"
25-26 = "25-26"
27-30 = "27-30"
31-34 = "31-34"
35-43 = "35-43"
44-51 = "44-51"
52-60 = "52-60"
61-64 = "61-64"
65-69 = "65-69"
70-81 = "70-81"
82-high = "82-";
run;
data polizzebyeta;
set polizzebyeta;
leveleta = eta;
format leveleta formateta.;
run;
proc means data = polizzebyeta nway noprint;
class leveleta;
var eta totfreqsin;
weight totespo;
output out = polizzebyleveleta1 mean = etamed totfreqsinmed;
run;
proc means data = polizzebyeta nway noprint;
class leveleta;
var totespo totnsin totdannotot totnpol;
output out = polizzebyleveleta2 sum = totespo totnsin totdannotot totnpol;
run;
data polizzebyleveleta;
merge polizzebyleveleta1 polizzebyleveleta2;
by leveleta;
drop _type_ _freq_;
run;
proc standard data = polizzebyleveleta out = polizzebyleveletastd mean = 0 std = 1;
weight totespo;
var etamed totfreqsinmed;
run;
data polizzebyleveletastd;
set polizzebyleveletastd;
format etamed 8.4;
format totfreqsinmed 8.4;
run;
data polizzebyleveletastd;
set polizzebyleveletastd;
rename totfreqsinmed = totfreqsinmedstd;
rename etamed = etamedstd;
run;
data polizzebyleveleta;
merge polizzebyleveleta polizzebyleveletastd;
by leveleta;
run;
proc print data = polizzebyleveleta;
run;
SAS Output
| 18-22 |
21 |
0.17877 |
6047.04 |
1081 |
4007061.49 |
8991 |
-0.0144 |
0.0323 |
| 23-24 |
24 |
0.14233 |
5290.49 |
753 |
2771965.77 |
7542 |
-0.0127 |
0.0168 |
| 25-26 |
26 |
0.12897 |
5807.76 |
749 |
2458076.42 |
8292 |
-0.0113 |
0.0111 |
| 27-30 |
29 |
0.10288 |
13053.90 |
1343 |
4436387.56 |
18671 |
-0.0093 |
-0.0000 |
| 31-34 |
32 |
0.09152 |
12992.03 |
1189 |
2940408.97 |
18382 |
-0.0067 |
-0.0049 |
| 35-43 |
39 |
0.08305 |
25371.75 |
2107 |
6632792.66 |
35267 |
-0.0025 |
-0.0085 |
| 44-51 |
47 |
0.10100 |
20356.78 |
2056 |
5287609.56 |
28264 |
0.0031 |
-0.0008 |
| 52-60 |
56 |
0.10451 |
17873.66 |
1868 |
5358383.58 |
24606 |
0.0087 |
0.0007 |
| 61-64 |
62 |
0.09028 |
5781.94 |
522 |
1467871.43 |
7813 |
0.0131 |
-0.0054 |
| 65-69 |
67 |
0.09161 |
5414.12 |
496 |
1130324.59 |
7296 |
0.0160 |
-0.0048 |
| 70-81 |
73 |
0.09878 |
4899.85 |
484 |
1486592.19 |
6508 |
0.0203 |
-0.0018 |
| 82- |
86 |
0.10941 |
393.00 |
43 |
95525.78 |
529 |
0.0284 |
0.0028 |
proc cluster method = ward data = polizzebyleveleta outtree = clustereta;
id leveleta;
var etamedstd totfreqsinmedstd;
freq totespo;
copy totespo totnsin totdannotot etamed totfreqsinmed;
run;
SAS Output
The CLUSTER Procedure
Ward's Minimum Variance Cluster Analysis
| 0.00012676 |
0.00007507 |
0.7103 |
0.7103 |
| 0.00005169 |
|
0.2897 |
1.0000 |
| 61-64 |
65-69 |
11195 |
0.0011 |
.999 |
|
| 70-81 |
82- |
5292 |
0.0014 |
.997 |
|
| 23-24 |
25-26 |
11097 |
0.0043 |
.993 |
|
| 27-30 |
31-34 |
26045 |
0.0089 |
.984 |
|
| CL11 |
CL10 |
16487 |
0.0090 |
.975 |
|
| 44-51 |
52-60 |
38229 |
0.0145 |
.961 |
|
| CL8 |
35-43 |
51416 |
0.0394 |
.921 |
|
| 18-22 |
CL9 |
17144 |
0.0621 |
.859 |
|
| CL6 |
CL7 |
54716 |
0.0694 |
.790 |
|
| CL5 |
CL3 |
106132 |
0.2665 |
.523 |
|
| CL4 |
CL2 |
123276 |
0.5234 |
.000 |
|
Con 9 cluster arrivo a $R^2 ≥ 0.99$
proc tree data = clustereta nclusters = 9 out = cluster9eta noprint;
id leveleta;
copy totespo totnsin totdannotot etamed totfreqsinmed;
run;
proc print data = cluster9eta;
run;
SAS Output
| 61-64 |
5781.94 |
522 |
1467871.43 |
62 |
0.09028 |
1 |
CL11 |
| 65-69 |
5414.12 |
496 |
1130324.59 |
67 |
0.09161 |
1 |
CL11 |
| 70-81 |
4899.85 |
484 |
1486592.19 |
73 |
0.09878 |
2 |
CL10 |
| 82- |
393.00 |
43 |
95525.78 |
86 |
0.10941 |
2 |
CL10 |
| 23-24 |
5290.49 |
753 |
2771965.77 |
24 |
0.14233 |
3 |
CL9 |
| 25-26 |
5807.76 |
749 |
2458076.42 |
26 |
0.12897 |
3 |
CL9 |
| 27-30 |
13053.90 |
1343 |
4436387.56 |
29 |
0.10288 |
4 |
27-30 |
| 31-34 |
12992.03 |
1189 |
2940408.97 |
32 |
0.09152 |
5 |
31-34 |
| 44-51 |
20356.78 |
2056 |
5287609.56 |
47 |
0.10100 |
6 |
44-51 |
| 52-60 |
17873.66 |
1868 |
5358383.58 |
56 |
0.10451 |
7 |
52-60 |
| 35-43 |
25371.75 |
2107 |
6632792.66 |
39 |
0.08305 |
8 |
35-43 |
| 18-22 |
6047.04 |
1081 |
4007061.49 |
21 |
0.17877 |
9 |
18-22 |
proc means data = cluster9eta nway noprint;
class cluster;
var totespo totnsin totdannotot;
output out = polizzebyclustereta sum = totespocl totnsincl totdannototcl;
run;
data polizzebyclustereta;
set polizzebyclustereta;
totfreqsincl = totnsincl/totespocl;
if totnsincl>0 then totdannomedcl = totdannototcl/totnsincl;
else totdannomedcl = 0;
totqdcl = totdannototcl / totespocl;
drop _type_;
format totfreqsincl 5.3;
format totespocl 10.2;
format totdannototcl 10.2;
format totqdcl 10.2;
run;
proc print data = polizzebyclustereta;
run;
SAS Output
| 1 |
2 |
11196.06 |
1018 |
2598196.02 |
0.091 |
2552.26 |
232.06 |
| 2 |
2 |
5292.85 |
527 |
1582117.97 |
0.100 |
3002.12 |
298.92 |
| 3 |
2 |
11098.25 |
1502 |
5230042.20 |
0.135 |
3482.05 |
471.25 |
| 4 |
1 |
13053.90 |
1343 |
4436387.56 |
0.103 |
3303.34 |
339.85 |
| 5 |
1 |
12992.03 |
1189 |
2940408.97 |
0.092 |
2473.01 |
226.32 |
| 6 |
1 |
20356.78 |
2056 |
5287609.56 |
0.101 |
2571.79 |
259.75 |
| 7 |
1 |
17873.66 |
1868 |
5358383.58 |
0.105 |
2868.51 |
299.79 |
| 8 |
1 |
25371.75 |
2107 |
6632792.66 |
0.083 |
3147.98 |
261.42 |
| 9 |
1 |
6047.04 |
1081 |
4007061.49 |
0.179 |
3706.81 |
662.65 |
proc sort data = cluster9eta;
by cluster;
run;
data cluster9eta;
merge cluster9eta polizzebyclustereta;
by cluster;
run;
proc print data = cluster9eta;
run;
SAS Output
| 61-64 |
5781.94 |
522 |
1467871.43 |
62 |
0.09028 |
1 |
CL11 |
2 |
11196.06 |
1018 |
2598196.02 |
0.091 |
2552.26 |
232.06 |
| 65-69 |
5414.12 |
496 |
1130324.59 |
67 |
0.09161 |
1 |
CL11 |
2 |
11196.06 |
1018 |
2598196.02 |
0.091 |
2552.26 |
232.06 |
| 70-81 |
4899.85 |
484 |
1486592.19 |
73 |
0.09878 |
2 |
CL10 |
2 |
5292.85 |
527 |
1582117.97 |
0.100 |
3002.12 |
298.92 |
| 82- |
393.00 |
43 |
95525.78 |
86 |
0.10941 |
2 |
CL10 |
2 |
5292.85 |
527 |
1582117.97 |
0.100 |
3002.12 |
298.92 |
| 23-24 |
5290.49 |
753 |
2771965.77 |
24 |
0.14233 |
3 |
CL9 |
2 |
11098.25 |
1502 |
5230042.20 |
0.135 |
3482.05 |
471.25 |
| 25-26 |
5807.76 |
749 |
2458076.42 |
26 |
0.12897 |
3 |
CL9 |
2 |
11098.25 |
1502 |
5230042.20 |
0.135 |
3482.05 |
471.25 |
| 27-30 |
13053.90 |
1343 |
4436387.56 |
29 |
0.10288 |
4 |
27-30 |
1 |
13053.90 |
1343 |
4436387.56 |
0.103 |
3303.34 |
339.85 |
| 31-34 |
12992.03 |
1189 |
2940408.97 |
32 |
0.09152 |
5 |
31-34 |
1 |
12992.03 |
1189 |
2940408.97 |
0.092 |
2473.01 |
226.32 |
| 44-51 |
20356.78 |
2056 |
5287609.56 |
47 |
0.10100 |
6 |
44-51 |
1 |
20356.78 |
2056 |
5287609.56 |
0.101 |
2571.79 |
259.75 |
| 52-60 |
17873.66 |
1868 |
5358383.58 |
56 |
0.10451 |
7 |
52-60 |
1 |
17873.66 |
1868 |
5358383.58 |
0.105 |
2868.51 |
299.79 |
| 35-43 |
25371.75 |
2107 |
6632792.66 |
39 |
0.08305 |
8 |
35-43 |
1 |
25371.75 |
2107 |
6632792.66 |
0.083 |
3147.98 |
261.42 |
| 18-22 |
6047.04 |
1081 |
4007061.49 |
21 |
0.17877 |
9 |
18-22 |
1 |
6047.04 |
1081 |
4007061.49 |
0.179 |
3706.81 |
662.65 |
2.3 potf
proc means data = polizze nway noprint;
class potf;
var espo nsin dannotot;
output out=polizzebypotf sum=totespo totnsin totdannotot;
run;
data polizzebypotf;
set polizzebypotf;
totfreqsin = totnsin / totespo;
if totnsin > 0 then totdannomed = totdannotot / totnsin;
else totdannomed = 0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
run;
proc print data = polizzebypotf (obs = 10) noobs;
var potf totfreqsin totdannomed totqd totespo;
run;
SAS Output
| 8 |
0.05539 |
1944.00 |
107.686 |
108.32 |
| 9 |
0.07350 |
2652.59 |
194.962 |
462.59 |
| 10 |
0.08866 |
2521.23 |
223.520 |
8798.13 |
| 11 |
0.07610 |
1693.54 |
128.886 |
604.43 |
| 12 |
0.08950 |
2387.18 |
213.641 |
23710.77 |
| 13 |
0.09886 |
2865.89 |
283.325 |
18773.85 |
| 14 |
0.10245 |
3726.90 |
381.824 |
9985.27 |
| 15 |
0.11341 |
2712.68 |
307.646 |
14425.51 |
| 16 |
0.09970 |
3201.22 |
319.150 |
6319.19 |
| 17 |
0.10883 |
3172.22 |
345.247 |
13543.50 |
proc sgplot data = polizzebypotf;
scatter x = potf y = totfreqsin / markerattrs=(symbol=CircleFilled);
series x = potf y = totfreqsin;
run;
SAS Output
proc format;
value formatpotf
low-13 = "8-13"
14-15 = "14-15"
16 = "16"
17-21 = "17-21"
22-23 = "22-23"
24-26 = "24-26"
27-28 = "27-28"
29-30 = "29-30"
31-high = "31-";
run;
data polizzebypotf;
set polizzebypotf;
levelpotf = potf;
format levelpotf formatpotf.;
run;
proc means data = polizzebypotf nway noprint;
class levelpotf;
var potf totfreqsin;
weight totespo;
output out = polizzebylevelpotf1 mean = potfmed totfreqsinmed;
run;
proc means data = polizzebypotf nway noprint;
class levelpotf;
var totespo totnsin totdannotot totnpol;
output out = polizzebylevelpotf2 sum = totespo totnsin totdannotot totnpol;
run;
data polizzebylevelpotf;
merge polizzebylevelpotf1 polizzebylevelpotf2;
by levelpotf;
drop _type_ _freq_;
run;
proc standard data = polizzebylevelpotf out = polizzebylevelpotfstd mean = 0 std = 1;
weight totespo;
var potfmed totfreqsinmed;
run;
data polizzebylevelpotfstd;
set polizzebylevelpotfstd;
format potfmed 8.4;
format totfreqsinmed 8.4;
run;
data polizzebylevelpotfstd;
set polizzebylevelpotfstd;
rename totfreqsinmed = totfreqsinmedstd;
rename potfmed = potfmedstd;
run;
data polizzebylevelpotf;
merge polizzebylevelpotf polizzebylevelpotfstd;
by levelpotf;
run;
proc print data = polizzebylevelpotf;
run;
SAS Output
| 8-13 |
11.9762 |
0.09234 |
52458.09 |
4844 |
12530996.69 |
69752 |
-0.0078 |
-0.0072 |
| 14-15 |
14.5909 |
0.10893 |
24410.77 |
2659 |
8250561.58 |
33959 |
-0.0007 |
0.0040 |
| 16 |
16.0000 |
0.09970 |
6319.19 |
630 |
2016770.78 |
8812 |
0.0031 |
-0.0022 |
| 17-21 |
18.2424 |
0.11131 |
37795.14 |
4207 |
14159780.22 |
55913 |
0.0092 |
0.0057 |
| 22-23 |
22.8791 |
0.16838 |
1829.25 |
308 |
880999.10 |
2911 |
0.0217 |
0.0442 |
| 24-26 |
25.7794 |
0.10898 |
211.05 |
23 |
153340.75 |
350 |
0.0295 |
0.0041 |
| 27-28 |
27.5069 |
0.07383 |
40.63 |
3 |
32992.87 |
74 |
0.0342 |
-0.0197 |
| 29-30 |
29.5077 |
0.07867 |
114.40 |
9 |
31938.14 |
203 |
0.0396 |
-0.0164 |
| 31- |
35.2581 |
0.07708 |
103.79 |
8 |
15619.88 |
187 |
0.0552 |
-0.0175 |
proc cluster method = ward data = polizzebylevelpotf outtree = clusterpotf;
id levelpotf;
var potfmedstd totfreqsinmedstd;
freq totespo;
copy totespo totnsin totdannotot potfmed totfreqsinmed;
run;
SAS Output
The CLUSTER Procedure
Ward's Minimum Variance Cluster Analysis
| 0.00011638 |
0.00010301 |
0.8970 |
0.8970 |
| 0.00001337 |
|
0.1030 |
1.0000 |
| 27-28 |
29-30 |
154 |
0.0001 |
1.00 |
|
| CL8 |
31- |
257 |
0.0011 |
.999 |
|
| 24-26 |
CL7 |
468 |
0.0051 |
.994 |
|
| 14-15 |
16 |
30729 |
0.0168 |
.977 |
|
| 17-21 |
CL6 |
38263 |
0.0292 |
.948 |
|
| CL5 |
CL4 |
68992 |
0.1028 |
.845 |
|
| CL3 |
22-23 |
70821 |
0.2078 |
.637 |
|
| 8-13 |
CL2 |
123279 |
0.6371 |
.000 |
|
Con 6 cluster arrivo a $R^2 ≥ 0.99$
proc tree data = clusterpotf nclusters = 6 out = cluster6potf noprint;
id levelpotf;
copy totespo totnsin totdannotot potfmed totfreqsinmed;
run;
proc print data = cluster9eta;
run;
SAS Output
| 61-64 |
5781.94 |
522 |
1467871.43 |
62 |
0.09028 |
1 |
CL11 |
2 |
11196.06 |
1018 |
2598196.02 |
0.091 |
2552.26 |
232.06 |
| 65-69 |
5414.12 |
496 |
1130324.59 |
67 |
0.09161 |
1 |
CL11 |
2 |
11196.06 |
1018 |
2598196.02 |
0.091 |
2552.26 |
232.06 |
| 70-81 |
4899.85 |
484 |
1486592.19 |
73 |
0.09878 |
2 |
CL10 |
2 |
5292.85 |
527 |
1582117.97 |
0.100 |
3002.12 |
298.92 |
| 82- |
393.00 |
43 |
95525.78 |
86 |
0.10941 |
2 |
CL10 |
2 |
5292.85 |
527 |
1582117.97 |
0.100 |
3002.12 |
298.92 |
| 23-24 |
5290.49 |
753 |
2771965.77 |
24 |
0.14233 |
3 |
CL9 |
2 |
11098.25 |
1502 |
5230042.20 |
0.135 |
3482.05 |
471.25 |
| 25-26 |
5807.76 |
749 |
2458076.42 |
26 |
0.12897 |
3 |
CL9 |
2 |
11098.25 |
1502 |
5230042.20 |
0.135 |
3482.05 |
471.25 |
| 27-30 |
13053.90 |
1343 |
4436387.56 |
29 |
0.10288 |
4 |
27-30 |
1 |
13053.90 |
1343 |
4436387.56 |
0.103 |
3303.34 |
339.85 |
| 31-34 |
12992.03 |
1189 |
2940408.97 |
32 |
0.09152 |
5 |
31-34 |
1 |
12992.03 |
1189 |
2940408.97 |
0.092 |
2473.01 |
226.32 |
| 44-51 |
20356.78 |
2056 |
5287609.56 |
47 |
0.10100 |
6 |
44-51 |
1 |
20356.78 |
2056 |
5287609.56 |
0.101 |
2571.79 |
259.75 |
| 52-60 |
17873.66 |
1868 |
5358383.58 |
56 |
0.10451 |
7 |
52-60 |
1 |
17873.66 |
1868 |
5358383.58 |
0.105 |
2868.51 |
299.79 |
| 35-43 |
25371.75 |
2107 |
6632792.66 |
39 |
0.08305 |
8 |
35-43 |
1 |
25371.75 |
2107 |
6632792.66 |
0.083 |
3147.98 |
261.42 |
| 18-22 |
6047.04 |
1081 |
4007061.49 |
21 |
0.17877 |
9 |
18-22 |
1 |
6047.04 |
1081 |
4007061.49 |
0.179 |
3706.81 |
662.65 |
proc means data = cluster6potf nway noprint;
class cluster;
var totespo totnsin totdannotot;
output out = polizzebyclusterpotf sum = totespocl totnsincl totdannototcl;
run;
data polizzebyclusterpotf;
set polizzebyclusterpotf;
totfreqsincl = totnsincl / totespocl;
if totnsincl > 0 then totdannomedcl = totdannototcl / totnsincl;
else totdannomedcl = 0;
totqdcl = totdannototcl / totespocl;
drop _type_;
format totfreqsincl 5.3;
format totespocl 10.2;
format totdannototcl 10.2;
format totqdcl 10.2;
run;
proc print data = polizzebyclusterpotf;
run;
SAS Output
| 1 |
4 |
469.88 |
43 |
233891.63 |
0.092 |
5439.34 |
497.77 |
| 2 |
1 |
24410.77 |
2659 |
8250561.58 |
0.109 |
3102.88 |
337.99 |
| 3 |
1 |
6319.19 |
630 |
2016770.78 |
0.100 |
3201.22 |
319.15 |
| 4 |
1 |
37795.14 |
4207 |
14159780.2 |
0.111 |
3365.77 |
374.65 |
| 5 |
1 |
1829.25 |
308 |
880999.10 |
0.168 |
2860.39 |
481.62 |
| 6 |
1 |
52458.09 |
4844 |
12530996.7 |
0.092 |
2586.91 |
238.88 |
proc sort data = cluster6potf;
by cluster;
run;
data cluster6potf;
merge cluster6potf polizzebyclusterpotf;
by cluster;
run;
proc print data = cluster6potf;
run;
SAS Output
| 27-28 |
40.63 |
3 |
32992.87 |
27.5069 |
0.07383 |
1 |
CL6 |
4 |
469.88 |
43 |
233891.63 |
0.092 |
5439.34 |
497.77 |
| 29-30 |
114.40 |
9 |
31938.14 |
29.5077 |
0.07867 |
1 |
CL6 |
4 |
469.88 |
43 |
233891.63 |
0.092 |
5439.34 |
497.77 |
| 31- |
103.79 |
8 |
15619.88 |
35.2581 |
0.07708 |
1 |
CL6 |
4 |
469.88 |
43 |
233891.63 |
0.092 |
5439.34 |
497.77 |
| 24-26 |
211.05 |
23 |
153340.75 |
25.7794 |
0.10898 |
1 |
CL6 |
4 |
469.88 |
43 |
233891.63 |
0.092 |
5439.34 |
497.77 |
| 14-15 |
24410.77 |
2659 |
8250561.58 |
14.5909 |
0.10893 |
2 |
14-15 |
1 |
24410.77 |
2659 |
8250561.58 |
0.109 |
3102.88 |
337.99 |
| 16 |
6319.19 |
630 |
2016770.78 |
16.0000 |
0.09970 |
3 |
16 |
1 |
6319.19 |
630 |
2016770.78 |
0.100 |
3201.22 |
319.15 |
| 17-21 |
37795.14 |
4207 |
14159780.22 |
18.2424 |
0.11131 |
4 |
17-21 |
1 |
37795.14 |
4207 |
14159780.2 |
0.111 |
3365.77 |
374.65 |
| 22-23 |
1829.25 |
308 |
880999.10 |
22.8791 |
0.16838 |
5 |
22-23 |
1 |
1829.25 |
308 |
880999.10 |
0.168 |
2860.39 |
481.62 |
| 8-13 |
52458.09 |
4844 |
12530996.69 |
11.9762 |
0.09234 |
6 |
8-13 |
1 |
52458.09 |
4844 |
12530996.7 |
0.092 |
2586.91 |
238.88 |
2.4 potkil
proc means data = polizze nway noprint;
class potkil;
var espo nsin dannotot;
output out = polizzebypotkil sum = totespo totnsin totdannotot;
run;
data polizzebypotkil;
set polizzebypotkil;
totfreqsin = totnsin / totespo;
if totnsin > 0 then totdannomed = totdannotot / totnsin;
else totdannomed = 0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
run;
proc print data = polizzebypotkil (obs = 10) noobs;
var potkil totfreqsin totdannomed totqd totespo;
run;
SAS Output
| 17 |
0.00000 |
0.00 |
0.000 |
1.00 |
| 18 |
0.07744 |
1962.64 |
151.979 |
761.92 |
| 21 |
0.07948 |
1004.69 |
79.857 |
50.32 |
| 22 |
0.06481 |
2123.15 |
137.611 |
1388.58 |
| 23 |
0.06825 |
2928.59 |
199.878 |
424.90 |
| 24 |
0.04795 |
1232.91 |
59.115 |
166.85 |
| 25 |
0.09376 |
2565.60 |
240.549 |
7231.26 |
| 26 |
0.05409 |
1834.78 |
99.243 |
110.93 |
| 27 |
0.14576 |
1629.22 |
237.483 |
54.88 |
| 28 |
0.60132 |
1617.55 |
972.671 |
1.66 |
proc sgplot data = polizzebypotkil;
scatter x = potkil y = totfreqsin / markerattrs=(symbol=CircleFilled);
series x = potkil y = totfreqsin;
run;
SAS Output
proc format;
value formatpotkil
low-26 = "17-26"
27-33 = "27-33"
34-39 = "34-39"
40-49 = "40-49"
50-57 = "50-57"
58-65 = "58-65"
66-78 = "66-78"
79-92 = "79-92"
93-108 = "93-108"
109-123 = "109-123"
124-139 = "124-139"
140-143 = "140-143"
144-150 = "144-150"
151-high = "151-";
run;
data polizzebypotkil;
set polizzebypotkil;
levelpotkil = potkil;
format levelpotkil formatpotkil.;
run;
proc means data = polizzebypotkil nway noprint;
class levelpotkil;
var potkil totfreqsin;
weight totespo;
output out = polizzebylevelpotkil1 mean = potkilmed totfreqsinmed;
run;
proc means data = polizzebypotkil nway noprint;
class levelpotkil;
var totespo totnsin totdannotot totnpol;
output out = polizzebylevelpotkil2 sum = totespo totnsin totdannotot totnpol;
run;
data polizzebylevelpotkil;
merge polizzebylevelpotkil1 polizzebylevelpotkil2;
by levelpotkil;
drop _type_ _freq_;
run;
proc standard data = polizzebylevelpotkil out = polizzebylevelpotkilstd mean = 0 std = 1;
weight totespo;
var potkilmed totfreqsinmed;
run;
data polizzebylevelpotkilstd;
set polizzebylevelpotkilstd;;
format potkilmed 8.4;
format totfreqsinmed 8.4;
run;
data polizzebylevelpotkilstd;
set polizzebylevelpotkilstd;
rename totfreqsinmed = totfreqsinmedstd;
rename potkilmed = potkilmedstd;
run;
data polizzebylevelpotkil;
merge polizzebylevelpotkil polizzebylevelpotkilstd;
by levelpotkil;
run;
proc print data = polizzebylevelpotkil;
run;
SAS Output
| 17-26 |
24 |
0.08623 |
10135.77 |
874 |
2156174.24 |
12869 |
-0.0122 |
-0.0182 |
| 27-33 |
32 |
0.09524 |
25850.67 |
2462 |
6016100.65 |
33836 |
-0.0085 |
-0.0084 |
| 34-39 |
37 |
0.09485 |
8866.64 |
841 |
2349060.15 |
11897 |
-0.0066 |
-0.0088 |
| 40-49 |
42 |
0.10566 |
21947.98 |
2319 |
6765891.74 |
30871 |
-0.0042 |
0.0029 |
| 50-57 |
54 |
0.10234 |
18468.22 |
1890 |
6129883.56 |
26263 |
0.0011 |
-0.0007 |
| 58-65 |
63 |
0.11136 |
8961.77 |
998 |
2819251.65 |
12396 |
0.0049 |
0.0091 |
| 66-78 |
70 |
0.11802 |
13294.86 |
1569 |
5232526.19 |
19805 |
0.0084 |
0.0164 |
| 79-92 |
84 |
0.10980 |
8551.79 |
939 |
3712429.07 |
12715 |
0.0146 |
0.0074 |
| 93-108 |
100 |
0.11632 |
4556.23 |
530 |
1947041.86 |
7146 |
0.0215 |
0.0145 |
| 109-123 |
113 |
0.10033 |
1335.57 |
134 |
394231.62 |
2114 |
0.0275 |
-0.0028 |
| 124-139 |
133 |
0.10190 |
510.29 |
52 |
201130.36 |
827 |
0.0361 |
-0.0011 |
| 140-143 |
141 |
0.14247 |
42.11 |
6 |
8233.18 |
71 |
0.0397 |
0.0429 |
| 144-150 |
147 |
0.15611 |
224.20 |
35 |
144582.22 |
393 |
0.0422 |
0.0577 |
| 151- |
176 |
0.07833 |
536.23 |
42 |
196463.52 |
958 |
0.0551 |
-0.0267 |
proc cluster method = ward data = polizzebylevelpotkil outtree = clusterpotkil;
id levelpotkil;
var potkilmedstd totfreqsinmedstd;
freq totespo;
copy totespo totnsin totdannotot potkilmed totfreqsinmed;
run;
SAS Output
The CLUSTER Procedure
Ward's Minimum Variance Cluster Analysis
| 0.00017512 |
0.00013937 |
0.8305 |
0.8305 |
| 0.00003575 |
|
0.1695 |
1.0000 |
| 140-143 |
144-150 |
266 |
0.0003 |
1.00 |
|
| 27-33 |
34-39 |
34716 |
0.0010 |
.999 |
|
| 109-123 |
124-139 |
1845 |
0.0011 |
.998 |
|
| 79-92 |
93-108 |
13107 |
0.0112 |
.986 |
|
| 58-65 |
66-78 |
22255 |
0.0132 |
.973 |
|
| 40-49 |
50-57 |
40415 |
0.0156 |
.958 |
|
| CL11 |
151- |
2381 |
0.0196 |
.938 |
|
| CL10 |
CL13 |
13373 |
0.0269 |
.911 |
|
| 17-26 |
CL12 |
44851 |
0.0337 |
.877 |
|
| CL9 |
CL6 |
35628 |
0.0378 |
.840 |
|
| CL4 |
CL7 |
38009 |
0.0874 |
.752 |
|
| CL5 |
CL8 |
85266 |
0.1589 |
.593 |
|
| CL2 |
CL3 |
123275 |
0.5932 |
.000 |
|
Con 11 cluster arrivo a $R^2 ≥ 0.99$
proc tree data = clusterpotkil nclusters = 11 out = cluster11potkil noprint;
id levelpotkil;
copy totespo totnsin totdannotot potkilmed totfreqsinmed;
run;
proc print data = cluster11potkil;
run;
SAS Output
| 140-143 |
42.11 |
6 |
8233.18 |
141 |
0.14247 |
1 |
CL13 |
| 144-150 |
224.20 |
35 |
144582.22 |
147 |
0.15611 |
1 |
CL13 |
| 27-33 |
25850.67 |
2462 |
6016100.65 |
32 |
0.09524 |
2 |
CL12 |
| 34-39 |
8866.64 |
841 |
2349060.15 |
37 |
0.09485 |
2 |
CL12 |
| 109-123 |
1335.57 |
134 |
394231.62 |
113 |
0.10033 |
3 |
CL11 |
| 124-139 |
510.29 |
52 |
201130.36 |
133 |
0.10190 |
3 |
CL11 |
| 79-92 |
8551.79 |
939 |
3712429.07 |
84 |
0.10980 |
4 |
79-92 |
| 93-108 |
4556.23 |
530 |
1947041.86 |
100 |
0.11632 |
5 |
93-108 |
| 58-65 |
8961.77 |
998 |
2819251.65 |
63 |
0.11136 |
6 |
58-65 |
| 66-78 |
13294.86 |
1569 |
5232526.19 |
70 |
0.11802 |
7 |
66-78 |
| 40-49 |
21947.98 |
2319 |
6765891.74 |
42 |
0.10566 |
8 |
40-49 |
| 50-57 |
18468.22 |
1890 |
6129883.56 |
54 |
0.10234 |
9 |
50-57 |
| 151- |
536.23 |
42 |
196463.52 |
176 |
0.07833 |
10 |
151- |
| 17-26 |
10135.77 |
874 |
2156174.24 |
24 |
0.08623 |
11 |
17-26 |
proc means data = cluster11potkil nway noprint;
class cluster;
var totespo totnsin totdannotot;
output out = polizzebyclusterpotkil sum = totespocl totnsincl totdannototcl;
run;
data polizzebyclusterpotkil;
set polizzebyclusterpotkil;
totfreqsincl = totnsincl/totespocl;
if totnsincl > 0 then totdannomedcl = totdannototcl / totnsincl;
else totdannomedcl = 0;
totqdcl = totdannototcl / totespocl;
drop _type_;
format totfreqsincl 5.3;
format totespocl 10.2;
format totdannototcl 10.2;
format totqdcl 10.2;
run;
proc print data = polizzebyclusterpotkil;
run;
SAS Output
| 1 |
2 |
266.31 |
41 |
152815.40 |
0.154 |
3727.20 |
573.82 |
| 2 |
2 |
34717.32 |
3303 |
8365160.80 |
0.095 |
2532.59 |
240.95 |
| 3 |
2 |
1845.86 |
186 |
595361.98 |
0.101 |
3200.87 |
322.54 |
| 4 |
1 |
8551.79 |
939 |
3712429.07 |
0.110 |
3953.60 |
434.11 |
| 5 |
1 |
4556.23 |
530 |
1947041.86 |
0.116 |
3673.66 |
427.34 |
| 6 |
1 |
8961.77 |
998 |
2819251.65 |
0.111 |
2824.90 |
314.59 |
| 7 |
1 |
13294.86 |
1569 |
5232526.19 |
0.118 |
3334.94 |
393.58 |
| 8 |
1 |
21947.98 |
2319 |
6765891.74 |
0.106 |
2917.59 |
308.27 |
| 9 |
1 |
18468.22 |
1890 |
6129883.56 |
0.102 |
3243.32 |
331.92 |
| 10 |
1 |
536.23 |
42 |
196463.52 |
0.078 |
4677.70 |
366.38 |
| 11 |
1 |
10135.77 |
874 |
2156174.24 |
0.086 |
2467.02 |
212.73 |
proc sort data = cluster11potkil;
by cluster;
run;
data cluster11potkil;
merge cluster11potkil polizzebyclusterpotkil;
by cluster;
run;
proc print data = cluster11potkil;
run;
SAS Output
| 140-143 |
42.11 |
6 |
8233.18 |
141 |
0.14247 |
1 |
CL13 |
2 |
266.31 |
41 |
152815.40 |
0.154 |
3727.20 |
573.82 |
| 144-150 |
224.20 |
35 |
144582.22 |
147 |
0.15611 |
1 |
CL13 |
2 |
266.31 |
41 |
152815.40 |
0.154 |
3727.20 |
573.82 |
| 27-33 |
25850.67 |
2462 |
6016100.65 |
32 |
0.09524 |
2 |
CL12 |
2 |
34717.32 |
3303 |
8365160.80 |
0.095 |
2532.59 |
240.95 |
| 34-39 |
8866.64 |
841 |
2349060.15 |
37 |
0.09485 |
2 |
CL12 |
2 |
34717.32 |
3303 |
8365160.80 |
0.095 |
2532.59 |
240.95 |
| 109-123 |
1335.57 |
134 |
394231.62 |
113 |
0.10033 |
3 |
CL11 |
2 |
1845.86 |
186 |
595361.98 |
0.101 |
3200.87 |
322.54 |
| 124-139 |
510.29 |
52 |
201130.36 |
133 |
0.10190 |
3 |
CL11 |
2 |
1845.86 |
186 |
595361.98 |
0.101 |
3200.87 |
322.54 |
| 79-92 |
8551.79 |
939 |
3712429.07 |
84 |
0.10980 |
4 |
79-92 |
1 |
8551.79 |
939 |
3712429.07 |
0.110 |
3953.60 |
434.11 |
| 93-108 |
4556.23 |
530 |
1947041.86 |
100 |
0.11632 |
5 |
93-108 |
1 |
4556.23 |
530 |
1947041.86 |
0.116 |
3673.66 |
427.34 |
| 58-65 |
8961.77 |
998 |
2819251.65 |
63 |
0.11136 |
6 |
58-65 |
1 |
8961.77 |
998 |
2819251.65 |
0.111 |
2824.90 |
314.59 |
| 66-78 |
13294.86 |
1569 |
5232526.19 |
70 |
0.11802 |
7 |
66-78 |
1 |
13294.86 |
1569 |
5232526.19 |
0.118 |
3334.94 |
393.58 |
| 40-49 |
21947.98 |
2319 |
6765891.74 |
42 |
0.10566 |
8 |
40-49 |
1 |
21947.98 |
2319 |
6765891.74 |
0.106 |
2917.59 |
308.27 |
| 50-57 |
18468.22 |
1890 |
6129883.56 |
54 |
0.10234 |
9 |
50-57 |
1 |
18468.22 |
1890 |
6129883.56 |
0.102 |
3243.32 |
331.92 |
| 151- |
536.23 |
42 |
196463.52 |
176 |
0.07833 |
10 |
151- |
1 |
536.23 |
42 |
196463.52 |
0.078 |
4677.70 |
366.38 |
| 17-26 |
10135.77 |
874 |
2156174.24 |
24 |
0.08623 |
11 |
17-26 |
1 |
10135.77 |
874 |
2156174.24 |
0.086 |
2467.02 |
212.73 |
2.5 massa
proc means data = polizze nway noprint;
class massa;
var espo nsin dannotot;
output out = polizzebymassa sum = totespo totnsin totdannotot;
run;
data polizzebymassa;
set polizzebymassa;
totfreqsin = totnsin / totespo;
if totnsin > 0 then totdannomed = totdannotot / totnsin;
else totdannomed = 0;
totqd = totdannotot / totespo;
drop _TYPE_;
rename _FREQ_ = totnpol;
run;
proc print data = polizzebymassa (obs = 10) noobs;
var massa totfreqsin totdannomed totqd totespo;
run;
SAS Output
| 555 |
0.00000 |
0.00 |
0.000 |
3.293 |
| 595 |
0.08505 |
1004.69 |
85.449 |
47.031 |
| 600 |
0.00000 |
0.00 |
0.000 |
1.000 |
| 620 |
0.07744 |
1962.64 |
151.979 |
761.919 |
| 640 |
0.10040 |
2535.30 |
254.545 |
597.609 |
| 645 |
0.09502 |
3869.34 |
367.668 |
210.480 |
| 650 |
0.06461 |
2292.56 |
148.115 |
386.957 |
| 655 |
0.08441 |
2658.69 |
224.424 |
485.715 |
| 660 |
0.09553 |
4501.34 |
430.005 |
83.745 |
| 665 |
0.16397 |
1850.27 |
303.397 |
12.197 |
proc sgplot data = polizzebymassa;
scatter x = massa y = totfreqsin / markerattrs=(symbol=CircleFilled);
series x = massa y = totfreqsin;
run;
SAS Output
proc format;
value formatmassa
low-691 = "555-691"
692-720 = "692-720"
721-800 = "721-800"
801-905 = "801-905"
906-980 = "906-980"
981-1030 = "981-1030"
1031-1094 = "1031-1094"
1095-1269 = "1095-1269"
1270-1379 = "1270-1379"
1380-1424 = "1380-1424"
1425-1520 = "1425-1520"
1521-high = "1521-";
run;
data polizzebymassa;
set polizzebymassa;
levelmassa = massa;
format levelmassa formatmassa.;
run;
proc means data = polizzebymassa nway noprint;
class levelmassa;
var massa totfreqsin;
weight totespo;
output out = polizzebylevelmassa1 mean = massamed totfreqsinmed;
run;
proc means data = polizzebymassa nway noprint;
class levelmassa;
var totespo totnsin totdannotot totnpol;
output out = polizzebylevelmassa2 sum = totespo totnsin totdannotot totnpol;
run;
data polizzebylevelmassa;
merge polizzebylevelmassa1 polizzebylevelmassa2;
by levelmassa;
drop _type_ _freq_;
run;
proc standard data = polizzebylevelmassa out = polizzebylevelmassastd mean = 0 std = 1;
weight totespo;
var massamed totfreqsinmed;
run;
data polizzebylevelmassastd;
set polizzebylevelmassastd;
rename totfreqsinmed = totfreqsinmedstd;
rename massamed = massamedstd;
run;
data polizzebylevelmassa;
merge polizzebylevelmassa polizzebylevelmassastd;
by levelmassa;
run;
proc print data = polizzebylevelmassastd;
run;
SAS Output
| 555-691 |
-0 |
-0.020622 |
5521.44 |
451 |
1061529.72 |
7300 |
| 692-720 |
-0 |
-0.012126 |
16065.77 |
1453 |
3658464.65 |
20597 |
| 721-800 |
-0 |
-0.004167 |
26549.50 |
2619 |
7429810.95 |
35149 |
| 801-905 |
-0 |
0.006782 |
19165.92 |
2107 |
5922241.99 |
27196 |
| 906-980 |
0 |
0.011072 |
12906.82 |
1476 |
5335631.45 |
18596 |
| 981-1030 |
0 |
-0.001131 |
11711.90 |
1192 |
3311423.85 |
16285 |
| 1031-1094 |
0 |
-0.001358 |
7287.62 |
740 |
1931281.76 |
10485 |
| 1095-1269 |
0 |
0.004669 |
16323.80 |
1759 |
6695084.72 |
24090 |
| 1270-1379 |
0 |
0.008103 |
4483.50 |
499 |
1539118.74 |
7006 |
| 1380-1424 |
0 |
-0.014131 |
1052.35 |
93 |
327804.52 |
1706 |
| 1425-1520 |
0 |
0.026959 |
1499.20 |
196 |
581444.16 |
2531 |
| 1521- |
0 |
0.044047 |
714.50 |
106 |
279163.49 |
1220 |
proc cluster method = ward data = polizzebylevelmassa outtree = clustermassa;
id levelmassa;
var massamedstd totfreqsinmedstd;
freq totespo;
copy totespo totnsin totdannotot massamed totfreqsinmed;
run;
SAS Output
The CLUSTER Procedure
Ward's Minimum Variance Cluster Analysis
| 0.00014846 |
0.00011849 |
0.8320 |
0.8320 |
| 0.00002998 |
|
0.1680 |
1.0000 |
| 981-1030 |
1031-1094 |
18998 |
0.0016 |
.998 |
|
| 1095-1269 |
1270-1379 |
20806 |
0.0083 |
.990 |
|
| 1425-1520 |
1521- |
2213 |
0.0108 |
.979 |
|
| 801-905 |
906-980 |
32071 |
0.0114 |
.968 |
|
| 555-691 |
692-720 |
21586 |
0.0143 |
.954 |
|
| CL10 |
1380-1424 |
21858 |
0.0217 |
.932 |
|
| CL11 |
CL6 |
40856 |
0.0490 |
.883 |
|
| CL7 |
721-800 |
48135 |
0.0627 |
.820 |
|
| CL5 |
CL9 |
43069 |
0.1295 |
.691 |
|
| CL8 |
CL3 |
75140 |
0.1453 |
.545 |
|
| CL4 |
CL2 |
123275 |
0.5455 |
.000 |
|
Con 10 cluster arrivo a $R^2 ≥ 0.99$
proc tree data = clustermassa nclusters = 10 out = cluster10massa noprint;
id levelmassa;
copy totespo totnsin totdannotot massamed totfreqsinmed;
run;
proc print data = cluster10massa;
run;
SAS Output
| 981-1030 |
11711.90 |
1192 |
3311423.85 |
1007 |
0.10178 |
1 |
CL11 |
| 1031-1094 |
7287.62 |
740 |
1931281.76 |
1065 |
0.10154 |
1 |
CL11 |
| 1095-1269 |
16323.80 |
1759 |
6695084.72 |
1171 |
0.10776 |
2 |
CL10 |
| 1270-1379 |
4483.50 |
499 |
1539118.74 |
1303 |
0.11130 |
2 |
CL10 |
| 1425-1520 |
1499.20 |
196 |
581444.16 |
1459 |
0.13074 |
3 |
1425-1520 |
| 1521- |
714.50 |
106 |
279163.49 |
1757 |
0.14835 |
4 |
1521- |
| 801-905 |
19165.92 |
2107 |
5922241.99 |
860 |
0.10993 |
5 |
801-905 |
| 906-980 |
12906.82 |
1476 |
5335631.45 |
939 |
0.11436 |
6 |
906-980 |
| 555-691 |
5521.44 |
451 |
1061529.72 |
663 |
0.08168 |
7 |
555-691 |
| 692-720 |
16065.77 |
1453 |
3658464.65 |
706 |
0.09044 |
8 |
692-720 |
| 1380-1424 |
1052.35 |
93 |
327804.52 |
1404 |
0.08837 |
9 |
1380-1424 |
| 721-800 |
26549.50 |
2619 |
7429810.95 |
772 |
0.09865 |
10 |
721-800 |
proc means data = cluster10massa nway noprint;
class cluster;
var totespo totnsin totdannotot;
output out = polizzebyclustermassa sum = totespocl totnsincl totdannototcl;
run;
data polizzebyclustermassa;
set polizzebyclustermassa;
totfreqsincl = totnsincl / totespocl;
if totnsincl > 0 then totdannomedcl = totdannototcl / totnsincl;
else totdannomedcl = 0;
totqdcl = totdannototcl / totespocl;
drop _type_;
format totfreqsincl 5.3;
format totespocl 10.2;
format totdannototcl 10.2;
format totqdcl 10.2;
run;
proc print data = polizzebyclustermassa;
run;
SAS Output
| 1 |
2 |
18999.52 |
1932 |
5242705.61 |
0.102 |
2713.62 |
275.94 |
| 2 |
2 |
20807.30 |
2258 |
8234203.46 |
0.109 |
3646.68 |
395.74 |
| 3 |
1 |
1499.20 |
196 |
581444.16 |
0.131 |
2966.55 |
387.84 |
| 4 |
1 |
714.50 |
106 |
279163.49 |
0.148 |
2633.62 |
390.71 |
| 5 |
1 |
19165.92 |
2107 |
5922241.99 |
0.110 |
2810.75 |
309.00 |
| 6 |
1 |
12906.82 |
1476 |
5335631.45 |
0.114 |
3614.93 |
413.40 |
| 7 |
1 |
5521.44 |
451 |
1061529.72 |
0.082 |
2353.72 |
192.26 |
| 8 |
1 |
16065.77 |
1453 |
3658464.65 |
0.090 |
2517.87 |
227.72 |
| 9 |
1 |
1052.35 |
93 |
327804.52 |
0.088 |
3524.78 |
311.50 |
| 10 |
1 |
26549.50 |
2619 |
7429810.95 |
0.099 |
2836.89 |
279.85 |
proc sort data = cluster10massa;
by cluster;
run;
data cluster10massa;
merge cluster10massa polizzebyclustermassa;
by cluster;
run;
proc print data = cluster10massa;
run;
SAS Output
| 981-1030 |
11711.90 |
1192 |
3311423.85 |
1007 |
0.10178 |
1 |
CL11 |
2 |
18999.52 |
1932 |
5242705.61 |
0.102 |
2713.62 |
275.94 |
| 1031-1094 |
7287.62 |
740 |
1931281.76 |
1065 |
0.10154 |
1 |
CL11 |
2 |
18999.52 |
1932 |
5242705.61 |
0.102 |
2713.62 |
275.94 |
| 1095-1269 |
16323.80 |
1759 |
6695084.72 |
1171 |
0.10776 |
2 |
CL10 |
2 |
20807.30 |
2258 |
8234203.46 |
0.109 |
3646.68 |
395.74 |
| 1270-1379 |
4483.50 |
499 |
1539118.74 |
1303 |
0.11130 |
2 |
CL10 |
2 |
20807.30 |
2258 |
8234203.46 |
0.109 |
3646.68 |
395.74 |
| 1425-1520 |
1499.20 |
196 |
581444.16 |
1459 |
0.13074 |
3 |
1425-1520 |
1 |
1499.20 |
196 |
581444.16 |
0.131 |
2966.55 |
387.84 |
| 1521- |
714.50 |
106 |
279163.49 |
1757 |
0.14835 |
4 |
1521- |
1 |
714.50 |
106 |
279163.49 |
0.148 |
2633.62 |
390.71 |
| 801-905 |
19165.92 |
2107 |
5922241.99 |
860 |
0.10993 |
5 |
801-905 |
1 |
19165.92 |
2107 |
5922241.99 |
0.110 |
2810.75 |
309.00 |
| 906-980 |
12906.82 |
1476 |
5335631.45 |
939 |
0.11436 |
6 |
906-980 |
1 |
12906.82 |
1476 |
5335631.45 |
0.114 |
3614.93 |
413.40 |
| 555-691 |
5521.44 |
451 |
1061529.72 |
663 |
0.08168 |
7 |
555-691 |
1 |
5521.44 |
451 |
1061529.72 |
0.082 |
2353.72 |
192.26 |
| 692-720 |
16065.77 |
1453 |
3658464.65 |
706 |
0.09044 |
8 |
692-720 |
1 |
16065.77 |
1453 |
3658464.65 |
0.090 |
2517.87 |
227.72 |
| 1380-1424 |
1052.35 |
93 |
327804.52 |
1404 |
0.08837 |
9 |
1380-1424 |
1 |
1052.35 |
93 |
327804.52 |
0.088 |
3524.78 |
311.50 |
| 721-800 |
26549.50 |
2619 |
7429810.95 |
772 |
0.09865 |
10 |
721-800 |
1 |
26549.50 |
2619 |
7429810.95 |
0.099 |
2836.89 |
279.85 |
proc format;
value $classprov
"RC","VT","CN","OR","RA","VC","FE","LC","SS","VV","BZ","PV","RG","CH","PG","AR","TE","TN","VR" = "prov1"
"BN","PO","IM","BA" = "prov2"
"EN","NO","SV","VI","MC","MT","RE","BS","RI","AG","AV","PC" = "prov3"
"AL","SO","GO","LT","PR","PN","GR","UD","TV","PD" = "prov4"
"SI","TR","AP","LO","FG","ME","LU","CZ","FR","CT","VE","BG","IS","MO","TP" = "prov5"
"CL","PI","VA","BR","FO","LI","SR","CO","SA" = "prov6"
"LE","RN","AN","MS","BO","GE","TS" = "prov7"
"CB","FI","NU","PE","TO","MI" = "prov8"
"PT","TA","SP","CA","ROMA","PA" = "prov9"
"BL","PZ","BI","CR","CS","AT","MN","PS" = "prov10"
"AO","NA","CE","KR" = "prov11"
"AQ","RSM","VB","RO" = "prov12";
run;
proc format;
value classeta
low-22 = "18-22"
23-26 = "23-26"
27-30 = "27-30"
31-34 = "31-34"
35-43 = "35-43"
44-51 = "44-51"
52-60 = "52-60"
61-69 = "61-69"
70-high = "70-";
run;
proc format;
value classpotf
low-13 = "8-13"
14-15 = "14-15"
16 = "16"
17-21 = "17-21"
22-23 = "22-23"
24-26 = "24-26"
27-28 = "27-28"
29-30 = "29-30"
31-high = "31-";
run;
proc format;
value classpotkil
low-26 = "17-26"
27-33 = "27-33"
34-39 = "34-39"
40-49 = "40-49"
50-57 = "50-57"
58-65 = "58-65"
66-78 = "66-78"
79-92 = "79-92"
93-108 = "93-108"
109-123 = "109-123"
124-139 = "124-139"
140-143 = "140-143"
144-150 = "144-150"
151-high = "151-";
run;
proc format;
value classmassa
low-691 = "555-691"
692-720 = "692-720"
721-800 = "721-800"
801-905 = "801-905"
906-980 = "906-980"
981-1030 = "981-1030"
1031-1094 = "1031-1094"
1095-1269 = "1095-1269"
1270-1379 = "1270-1379"
1380-1424 = "1380-1424"
1425-1520 = "1425-1520"
1521-high = "1521-";
run;
data polizze;
set polizze;
format prov $classprov.;
format eta classeta.;
format potf classpotf.;
format potkil classpotkil.;
format massa classmassa.;
run;
proc print data = polizze (obs = 10);
run;
SAS Output
| F |
35-43 |
prov8 |
NO |
B |
17-26 |
555-691 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
| M |
35-43 |
prov5 |
NO |
B |
34-39 |
721-800 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
| M |
44-51 |
prov7 |
NO |
B |
58-65 |
801-905 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
| F |
18-22 |
prov10 |
NO |
B |
34-39 |
692-720 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
| M |
44-51 |
prov9 |
NO |
B |
27-33 |
721-800 |
8-13 |
0.20000 |
0 |
0.000 |
0 |
| F |
44-51 |
prov8 |
NO |
B |
40-49 |
721-800 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
| M |
35-43 |
prov1 |
NO |
D |
50-57 |
1031-1094 |
17-21 |
1.00000 |
0 |
0.000 |
0 |
| M |
70- |
prov1 |
SI |
B |
58-65 |
906-980 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
| F |
44-51 |
prov1 |
NO |
B |
58-65 |
801-905 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
| M |
52-60 |
prov1 |
NO |
B |
79-92 |
1095-1269 |
17-21 |
1.00000 |
1 |
359.057 |
1 |
Frequenza sinistri nei cluster
proc sgplot data=polizze;
vline prov / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05;
run;
SAS Output
proc sgplot data=polizze;
vline eta / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05;
run;
SAS Output
proc sgplot data=polizze;
vline potf / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05;
run;
SAS Output
proc sgplot data=polizze;
vline potkil / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05;
run;
SAS Output
proc sgplot data=polizze;
vline massa / response=freqsin weight=espo stat=mean limitstat=clm alpha = .05;
run;
SAS Output
3) Tariffazione con i GLM
3.A.1 Modelli per il numero di sinistri
Preparazione dei dati
data polizze;
set polizze;
lnespo = log(espo);
freqsin = nsin / espo;
run;
proc means data = polizze nway noprint;
class sesso capoluogo bendie prov eta potf potkil massa;
var espo nsin dannotot;
output out = polizzecum sum = espocum nsincum dannototcum;
run;
data polizzecum;
set polizzecum;
lnespocum = log(espocum);
freqsincum = nsincum / espocum;
run;
proc print data = polizzecum (obs = 10);
run;
SAS Output
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
17-26 |
555-691 |
255 |
3 |
1.6880 |
0 |
0.00 |
0.52354 |
0.000000 |
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
17-26 |
692-720 |
255 |
23 |
18.9970 |
1 |
2019.70 |
2.94428 |
0.052640 |
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
27-33 |
555-691 |
255 |
4 |
3.3920 |
0 |
0.00 |
1.22142 |
0.000000 |
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
27-33 |
692-720 |
255 |
30 |
23.4110 |
0 |
0.00 |
3.15321 |
0.000000 |
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
27-33 |
721-800 |
255 |
64 |
46.9260 |
4 |
3753.05 |
3.84857 |
0.085241 |
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
27-33 |
906-980 |
255 |
1 |
0.9230 |
0 |
0.00 |
-0.08013 |
0.000000 |
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
34-39 |
692-720 |
255 |
7 |
5.6710 |
0 |
0.00 |
1.73537 |
0.000000 |
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
34-39 |
721-800 |
255 |
48 |
37.7090 |
3 |
4314.97 |
3.62990 |
0.079557 |
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
34-39 |
801-905 |
255 |
4 |
3.6740 |
0 |
0.00 |
1.30128 |
0.000000 |
| F |
NO |
B |
prov3 |
18-22 |
8-13 |
40-49 |
721-800 |
255 |
19 |
14.0980 |
1 |
394.96 |
2.64603 |
0.070932 |
proc summary data = polizzecum;
output out = conta_righe;
run;
proc print data = conta_righe;
run;
SAS Output
3.A.1.1 Modello di Poisson
proc genmod data = polizze;
class eta(ref='35-43');
model nsin = eta /
dist = poisson
offset = lnespo
type3;
run;
SAS Output
| WORK.POLIZZE |
| Poisson |
| Log |
| nsin |
| lnespo |
| 9 |
18-22 23-26 27-30 31-34 44-51 52-60 61-69 70- 35-43 |
| 17E4 |
66656.7461 |
0.3872 |
| 17E4 |
66656.7461 |
0.3872 |
| 17E4 |
211077.4956 |
1.2261 |
| 17E4 |
211077.4956 |
1.2261 |
| |
-44647.2568 |
|
| |
-45351.7365 |
|
| |
90721.4730 |
|
| |
90721.4740 |
|
| |
90811.9787 |
|
| |
1 |
-2.4884 |
0.0218 |
-2.5311 |
-2.4457 |
13046.5 |
<.0001 |
| 18-22 |
1 |
0.7667 |
0.0374 |
0.6934 |
0.8400 |
419.96 |
<.0001 |
| 23-26 |
1 |
0.4884 |
0.0338 |
0.4222 |
0.5546 |
209.15 |
<.0001 |
| 27-30 |
1 |
0.2142 |
0.0349 |
0.1458 |
0.2826 |
37.63 |
<.0001 |
| 31-34 |
1 |
0.0971 |
0.0363 |
0.0261 |
0.1682 |
7.17 |
0.0074 |
| 44-51 |
1 |
0.1957 |
0.0310 |
0.1350 |
0.2565 |
39.86 |
<.0001 |
| 52-60 |
1 |
0.2299 |
0.0318 |
0.1676 |
0.2922 |
52.34 |
<.0001 |
| 61-69 |
1 |
0.0906 |
0.0382 |
0.0158 |
0.1655 |
5.64 |
0.0176 |
| 70- |
1 |
0.1815 |
0.0487 |
0.0860 |
0.2769 |
13.88 |
0.0002 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
proc genmod data = polizzecum;
class eta(ref='35-43');
model nsincum = eta /
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 9 |
18-22 23-26 27-30 31-34 44-51 52-60 61-69 70- 35-43 |
| 26E3 |
20367.2147 |
0.7762 |
| 26E3 |
20367.2147 |
0.7762 |
| 26E3 |
39689.2852 |
1.5125 |
| 26E3 |
39689.2852 |
1.5125 |
| |
-11513.4125 |
|
| |
-18243.0724 |
|
| |
36504.1449 |
|
| |
36504.1517 |
|
| |
36577.7233 |
|
| |
1 |
-2.4884 |
0.0218 |
-2.5311 |
-2.4457 |
13046.5 |
<.0001 |
| 18-22 |
1 |
0.7667 |
0.0374 |
0.6934 |
0.8400 |
419.96 |
<.0001 |
| 23-26 |
1 |
0.4884 |
0.0338 |
0.4222 |
0.5546 |
209.15 |
<.0001 |
| 27-30 |
1 |
0.2142 |
0.0349 |
0.1458 |
0.2826 |
37.63 |
<.0001 |
| 31-34 |
1 |
0.0971 |
0.0363 |
0.0261 |
0.1682 |
7.17 |
0.0074 |
| 44-51 |
1 |
0.1957 |
0.0310 |
0.1350 |
0.2565 |
39.86 |
<.0001 |
| 52-60 |
1 |
0.2299 |
0.0318 |
0.1676 |
0.2922 |
52.34 |
<.0001 |
| 61-69 |
1 |
0.0906 |
0.0382 |
0.0158 |
0.1655 |
5.64 |
0.0176 |
| 70- |
1 |
0.1815 |
0.0487 |
0.0860 |
0.2769 |
13.88 |
0.0002 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
proc genmod data = polizzecum;
class eta(ref='35-43') potkil(ref='66-78');
model nsincum = eta potkil /
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 9 |
18-22 23-26 27-30 31-34 44-51 52-60 61-69 70- 35-43 |
| 14 |
109-123 124-139 140-143 144-150 151- 17-26 27-33 34-39 40-49 50-57 58-65 79-92 93-108 66-78 |
| 26E3 |
20231.0225 |
0.7714 |
| 26E3 |
20231.0225 |
0.7714 |
| 26E3 |
38161.8840 |
1.4551 |
| 26E3 |
38161.8840 |
1.4551 |
| |
-11445.3164 |
|
| |
-18174.9764 |
|
| |
36393.9527 |
|
| |
36393.9913 |
|
| |
36573.8111 |
|
| |
1 |
-2.3308 |
0.0317 |
-2.3929 |
-2.2687 |
5410.09 |
<.0001 |
| 18-22 |
1 |
0.7993 |
0.0376 |
0.7256 |
0.8731 |
451.02 |
<.0001 |
| 23-26 |
1 |
0.5031 |
0.0338 |
0.4368 |
0.5694 |
221.04 |
<.0001 |
| 27-30 |
1 |
0.2200 |
0.0349 |
0.1515 |
0.2885 |
39.66 |
<.0001 |
| 31-34 |
1 |
0.0980 |
0.0363 |
0.0269 |
0.1691 |
7.30 |
0.0069 |
| 44-51 |
1 |
0.1947 |
0.0310 |
0.1339 |
0.2555 |
39.42 |
<.0001 |
| 52-60 |
1 |
0.2362 |
0.0318 |
0.1739 |
0.2985 |
55.16 |
<.0001 |
| 61-69 |
1 |
0.1113 |
0.0382 |
0.0363 |
0.1862 |
8.47 |
0.0036 |
| 70- |
1 |
0.2174 |
0.0488 |
0.1217 |
0.3131 |
19.82 |
<.0001 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 109-123 |
1 |
-0.1738 |
0.0900 |
-0.3502 |
0.0027 |
3.73 |
0.0536 |
| 124-139 |
1 |
-0.1594 |
0.1410 |
-0.4356 |
0.1169 |
1.28 |
0.2583 |
| 140-143 |
1 |
0.1604 |
0.4090 |
-0.6413 |
0.9621 |
0.15 |
0.6949 |
| 144-150 |
1 |
0.2581 |
0.1709 |
-0.0769 |
0.5931 |
2.28 |
0.1310 |
| 151- |
1 |
-0.4037 |
0.1564 |
-0.7102 |
-0.0972 |
6.67 |
0.0098 |
| 17-26 |
1 |
-0.3305 |
0.0423 |
-0.4133 |
-0.2477 |
61.15 |
<.0001 |
| 27-33 |
1 |
-0.2620 |
0.0325 |
-0.3256 |
-0.1984 |
65.19 |
<.0001 |
| 34-39 |
1 |
-0.2846 |
0.0429 |
-0.3687 |
-0.2005 |
44.00 |
<.0001 |
| 40-49 |
1 |
-0.1597 |
0.0328 |
-0.2240 |
-0.0954 |
23.72 |
<.0001 |
| 50-57 |
1 |
-0.1673 |
0.0342 |
-0.2343 |
-0.1003 |
23.95 |
<.0001 |
| 58-65 |
1 |
-0.0596 |
0.0405 |
-0.1390 |
0.0198 |
2.17 |
0.1410 |
| 79-92 |
1 |
-0.0810 |
0.0413 |
-0.1619 |
-0.0001 |
3.85 |
0.0497 |
| 93-108 |
1 |
-0.0260 |
0.0503 |
-0.1245 |
0.0725 |
0.27 |
0.6055 |
| 66-78 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 8 |
548.35 |
<.0001 |
| 13 |
136.19 |
<.0001 |
proc genmod data = polizzecum;
class eta(ref='35-43') potkil(ref='66-78') massa(ref='906-980');
model nsincum = eta potkil massa /
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 9 |
18-22 23-26 27-30 31-34 44-51 52-60 61-69 70- 35-43 |
| 14 |
109-123 124-139 140-143 144-150 151- 17-26 27-33 34-39 40-49 50-57 58-65 79-92 93-108 66-78 |
| 12 |
1031-1094 1095-1269 1270-1379 1380-1424 1425-1520 1521- 555-691 692-720 721-800 801-905 981-1030 906-980 |
| 26E3 |
20178.0174 |
0.7697 |
| 26E3 |
20178.0174 |
0.7697 |
| 26E3 |
37643.0704 |
1.4359 |
| 26E3 |
37643.0704 |
1.4359 |
| |
-11418.8138 |
|
| |
-18148.4738 |
|
| |
36362.9476 |
|
| |
36363.0332 |
|
| |
36632.7352 |
|
| |
1 |
-2.2876 |
0.0430 |
-2.3718 |
-2.2033 |
2832.47 |
<.0001 |
| 18-22 |
1 |
0.7991 |
0.0380 |
0.7247 |
0.8735 |
443.04 |
<.0001 |
| 23-26 |
1 |
0.5046 |
0.0341 |
0.4379 |
0.5714 |
219.49 |
<.0001 |
| 27-30 |
1 |
0.2227 |
0.0350 |
0.1541 |
0.2913 |
40.47 |
<.0001 |
| 31-34 |
1 |
0.1010 |
0.0363 |
0.0299 |
0.1722 |
7.75 |
0.0054 |
| 44-51 |
1 |
0.1930 |
0.0310 |
0.1322 |
0.2538 |
38.71 |
<.0001 |
| 52-60 |
1 |
0.2356 |
0.0318 |
0.1732 |
0.2980 |
54.80 |
<.0001 |
| 61-69 |
1 |
0.1111 |
0.0383 |
0.0361 |
0.1861 |
8.43 |
0.0037 |
| 70- |
1 |
0.2193 |
0.0489 |
0.1235 |
0.3151 |
20.13 |
<.0001 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 109-123 |
1 |
-0.2378 |
0.0925 |
-0.4192 |
-0.0565 |
6.61 |
0.0102 |
| 124-139 |
1 |
-0.2294 |
0.1432 |
-0.5100 |
0.0512 |
2.57 |
0.1091 |
| 140-143 |
1 |
0.0761 |
0.4097 |
-0.7269 |
0.8790 |
0.03 |
0.8527 |
| 144-150 |
1 |
0.1513 |
0.1739 |
-0.1896 |
0.4923 |
0.76 |
0.3843 |
| 151- |
1 |
-0.6593 |
0.1647 |
-0.9822 |
-0.3365 |
16.03 |
<.0001 |
| 17-26 |
1 |
-0.2049 |
0.0696 |
-0.3414 |
-0.0685 |
8.67 |
0.0032 |
| 27-33 |
1 |
-0.1956 |
0.0540 |
-0.3016 |
-0.0897 |
13.11 |
0.0003 |
| 34-39 |
1 |
-0.2438 |
0.0581 |
-0.3576 |
-0.1300 |
17.64 |
<.0001 |
| 40-49 |
1 |
-0.1569 |
0.0440 |
-0.2432 |
-0.0706 |
12.70 |
0.0004 |
| 50-57 |
1 |
-0.1634 |
0.0382 |
-0.2383 |
-0.0885 |
18.27 |
<.0001 |
| 58-65 |
1 |
-0.0505 |
0.0425 |
-0.1337 |
0.0328 |
1.41 |
0.2346 |
| 79-92 |
1 |
-0.0868 |
0.0417 |
-0.1685 |
-0.0051 |
4.34 |
0.0373 |
| 93-108 |
1 |
-0.0473 |
0.0538 |
-0.1527 |
0.0581 |
0.77 |
0.3791 |
| 66-78 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1031-1094 |
1 |
-0.1086 |
0.0461 |
-0.1990 |
-0.0182 |
5.55 |
0.0185 |
| 1095-1269 |
1 |
-0.0616 |
0.0393 |
-0.1387 |
0.0155 |
2.45 |
0.1175 |
| 1270-1379 |
1 |
0.0015 |
0.0585 |
-0.1132 |
0.1162 |
0.00 |
0.9799 |
| 1380-1424 |
1 |
-0.2159 |
0.1130 |
-0.4373 |
0.0055 |
3.65 |
0.0560 |
| 1425-1520 |
1 |
0.2228 |
0.0840 |
0.0581 |
0.3874 |
7.03 |
0.0080 |
| 1521- |
1 |
0.4026 |
0.1073 |
0.1924 |
0.6129 |
14.09 |
0.0002 |
| 555-691 |
1 |
-0.2393 |
0.0708 |
-0.3781 |
-0.1005 |
11.42 |
0.0007 |
| 692-720 |
1 |
-0.1379 |
0.0580 |
-0.2515 |
-0.0243 |
5.66 |
0.0174 |
| 721-800 |
1 |
-0.0946 |
0.0464 |
-0.1855 |
-0.0036 |
4.15 |
0.0416 |
| 801-905 |
1 |
-0.0154 |
0.0385 |
-0.0908 |
0.0599 |
0.16 |
0.6878 |
| 981-1030 |
1 |
-0.0867 |
0.0394 |
-0.1640 |
-0.0094 |
4.84 |
0.0279 |
| 906-980 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 8 |
537.11 |
<.0001 |
| 13 |
51.08 |
<.0001 |
| 11 |
53.01 |
<.0001 |
proc genmod data = polizzecum;
class eta(ref='35-43') potkil(ref='66-78') massa(ref='906-980') potf;
model nsincum = eta potkil massa potf/
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 9 |
18-22 23-26 27-30 31-34 44-51 52-60 61-69 70- 35-43 |
| 14 |
109-123 124-139 140-143 144-150 151- 17-26 27-33 34-39 40-49 50-57 58-65 79-92 93-108 66-78 |
| 12 |
1031-1094 1095-1269 1270-1379 1380-1424 1425-1520 1521- 555-691 692-720 721-800 801-905 981-1030 906-980 |
| 9 |
14-15 16 17-21 22-23 24-26 27-28 29-30 31- 8-13 |
| 26E3 |
20079.5225 |
0.7662 |
| 26E3 |
20079.5225 |
0.7662 |
| 26E3 |
36510.7622 |
1.3931 |
| 26E3 |
36510.7622 |
1.3931 |
| |
-11369.5664 |
|
| |
-18099.2263 |
|
| |
36280.4526 |
|
| |
36280.5841 |
|
| |
36615.6433 |
|
| |
1 |
-2.5882 |
0.0602 |
-2.7061 |
-2.4703 |
1851.24 |
<.0001 |
| 18-22 |
1 |
0.7942 |
0.0380 |
0.7198 |
0.8686 |
437.50 |
<.0001 |
| 23-26 |
1 |
0.4959 |
0.0341 |
0.4291 |
0.5627 |
211.78 |
<.0001 |
| 27-30 |
1 |
0.2150 |
0.0350 |
0.1464 |
0.2836 |
37.72 |
<.0001 |
| 31-34 |
1 |
0.0979 |
0.0363 |
0.0267 |
0.1690 |
7.27 |
0.0070 |
| 44-51 |
1 |
0.1919 |
0.0310 |
0.1311 |
0.2527 |
38.26 |
<.0001 |
| 52-60 |
1 |
0.2371 |
0.0318 |
0.1747 |
0.2995 |
55.49 |
<.0001 |
| 61-69 |
1 |
0.1149 |
0.0383 |
0.0399 |
0.1899 |
9.01 |
0.0027 |
| 70- |
1 |
0.2256 |
0.0489 |
0.1298 |
0.3215 |
21.30 |
<.0001 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 109-123 |
1 |
-0.1700 |
0.0934 |
-0.3531 |
0.0131 |
3.31 |
0.0688 |
| 124-139 |
1 |
-0.1686 |
0.1518 |
-0.4662 |
0.1289 |
1.23 |
0.2667 |
| 140-143 |
1 |
0.0173 |
0.4120 |
-0.7902 |
0.8249 |
0.00 |
0.9664 |
| 144-150 |
1 |
0.2577 |
0.1757 |
-0.0868 |
0.6021 |
2.15 |
0.1426 |
| 151- |
1 |
-0.4219 |
0.1931 |
-0.8004 |
-0.0434 |
4.77 |
0.0289 |
| 17-26 |
1 |
-0.0081 |
0.0742 |
-0.1536 |
0.1374 |
0.01 |
0.9132 |
| 27-33 |
1 |
-0.0074 |
0.0594 |
-0.1238 |
0.1089 |
0.02 |
0.9003 |
| 34-39 |
1 |
-0.0669 |
0.0624 |
-0.1892 |
0.0554 |
1.15 |
0.2835 |
| 40-49 |
1 |
-0.0389 |
0.0461 |
-0.1293 |
0.0514 |
0.71 |
0.3982 |
| 50-57 |
1 |
-0.1060 |
0.0398 |
-0.1839 |
-0.0280 |
7.10 |
0.0077 |
| 58-65 |
1 |
-0.0148 |
0.0428 |
-0.0987 |
0.0690 |
0.12 |
0.7285 |
| 79-92 |
1 |
-0.0985 |
0.0419 |
-0.1807 |
-0.0164 |
5.53 |
0.0187 |
| 93-108 |
1 |
-0.0164 |
0.0543 |
-0.1229 |
0.0900 |
0.09 |
0.7622 |
| 66-78 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1031-1094 |
1 |
-0.2098 |
0.0487 |
-0.3053 |
-0.1142 |
18.52 |
<.0001 |
| 1095-1269 |
1 |
-0.1972 |
0.0434 |
-0.2823 |
-0.1121 |
20.62 |
<.0001 |
| 1270-1379 |
1 |
-0.1783 |
0.0624 |
-0.3006 |
-0.0560 |
8.16 |
0.0043 |
| 1380-1424 |
1 |
-0.3791 |
0.1146 |
-0.6038 |
-0.1544 |
10.94 |
0.0009 |
| 1425-1520 |
1 |
-0.0592 |
0.0920 |
-0.2395 |
0.1212 |
0.41 |
0.5202 |
| 1521- |
1 |
0.0498 |
0.1262 |
-0.1976 |
0.2973 |
0.16 |
0.6930 |
| 555-691 |
1 |
-0.1430 |
0.0720 |
-0.2841 |
-0.0019 |
3.94 |
0.0470 |
| 692-720 |
1 |
-0.0287 |
0.0601 |
-0.1464 |
0.0890 |
0.23 |
0.6324 |
| 721-800 |
1 |
0.0150 |
0.0492 |
-0.0814 |
0.1113 |
0.09 |
0.7605 |
| 801-905 |
1 |
0.0366 |
0.0394 |
-0.0406 |
0.1138 |
0.86 |
0.3531 |
| 981-1030 |
1 |
-0.1363 |
0.0403 |
-0.2153 |
-0.0573 |
11.43 |
0.0007 |
| 906-980 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 14-15 |
1 |
0.2045 |
0.0378 |
0.1305 |
0.2786 |
29.34 |
<.0001 |
| 16 |
1 |
0.1562 |
0.0560 |
0.0464 |
0.2660 |
7.77 |
0.0053 |
| 17-21 |
1 |
0.4110 |
0.0514 |
0.3103 |
0.5117 |
64.01 |
<.0001 |
| 22-23 |
1 |
0.7827 |
0.0882 |
0.6098 |
0.9555 |
78.77 |
<.0001 |
| 24-26 |
1 |
0.4922 |
0.2383 |
0.0252 |
0.9592 |
4.27 |
0.0389 |
| 27-28 |
1 |
0.0035 |
0.6017 |
-1.1758 |
1.1829 |
0.00 |
0.9953 |
| 29-30 |
1 |
0.2932 |
0.3754 |
-0.4426 |
1.0289 |
0.61 |
0.4349 |
| 31- |
1 |
0.1805 |
0.4017 |
-0.6070 |
0.9679 |
0.20 |
0.6533 |
| 8-13 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 8 |
526.37 |
<.0001 |
| 13 |
25.04 |
0.0228 |
| 11 |
51.68 |
<.0001 |
| 8 |
98.49 |
<.0001 |
proc genmod data = polizzecum;
class eta(ref='35-43') potkil(ref='66-78') massa(ref='906-980') bendie;
model nsincum = eta potkil massa bendie /
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 9 |
18-22 23-26 27-30 31-34 44-51 52-60 61-69 70- 35-43 |
| 14 |
109-123 124-139 140-143 144-150 151- 17-26 27-33 34-39 40-49 50-57 58-65 79-92 93-108 66-78 |
| 12 |
1031-1094 1095-1269 1270-1379 1380-1424 1425-1520 1521- 555-691 692-720 721-800 801-905 981-1030 906-980 |
| 2 |
B D |
| 26E3 |
19964.4087 |
0.7616 |
| 26E3 |
19964.4087 |
0.7616 |
| 26E3 |
35130.4937 |
1.3401 |
| 26E3 |
35130.4937 |
1.3401 |
| |
-11312.0095 |
|
| |
-18041.6694 |
|
| |
36151.3389 |
|
| |
36151.4296 |
|
| |
36429.3019 |
|
| |
1 |
-1.8284 |
0.0522 |
-1.9308 |
-1.7260 |
1224.67 |
<.0001 |
| 18-22 |
1 |
0.7887 |
0.0380 |
0.7143 |
0.8631 |
431.53 |
<.0001 |
| 23-26 |
1 |
0.4885 |
0.0341 |
0.4217 |
0.5553 |
205.50 |
<.0001 |
| 27-30 |
1 |
0.2112 |
0.0350 |
0.1426 |
0.2798 |
36.38 |
<.0001 |
| 31-34 |
1 |
0.0929 |
0.0363 |
0.0217 |
0.1640 |
6.55 |
0.0105 |
| 44-51 |
1 |
0.1911 |
0.0310 |
0.1303 |
0.2519 |
37.97 |
<.0001 |
| 52-60 |
1 |
0.2374 |
0.0318 |
0.1750 |
0.2997 |
55.64 |
<.0001 |
| 61-69 |
1 |
0.1144 |
0.0383 |
0.0394 |
0.1894 |
8.94 |
0.0028 |
| 70- |
1 |
0.2273 |
0.0489 |
0.1316 |
0.3231 |
21.64 |
<.0001 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 109-123 |
1 |
-0.0330 |
0.0931 |
-0.2155 |
0.1494 |
0.13 |
0.7227 |
| 124-139 |
1 |
-0.0001 |
0.1437 |
-0.2817 |
0.2816 |
0.00 |
0.9997 |
| 140-143 |
1 |
0.2989 |
0.4098 |
-0.5043 |
1.1021 |
0.53 |
0.4658 |
| 144-150 |
1 |
0.3904 |
0.1741 |
0.0491 |
0.7317 |
5.02 |
0.0250 |
| 151- |
1 |
-0.3129 |
0.1654 |
-0.6370 |
0.0112 |
3.58 |
0.0585 |
| 17-26 |
1 |
-0.3231 |
0.0697 |
-0.4596 |
-0.1866 |
21.51 |
<.0001 |
| 27-33 |
1 |
-0.3169 |
0.0541 |
-0.4231 |
-0.2108 |
34.26 |
<.0001 |
| 34-39 |
1 |
-0.3685 |
0.0582 |
-0.4825 |
-0.2545 |
40.15 |
<.0001 |
| 40-49 |
1 |
-0.2533 |
0.0441 |
-0.3397 |
-0.1670 |
33.06 |
<.0001 |
| 50-57 |
1 |
-0.2147 |
0.0385 |
-0.2900 |
-0.1393 |
31.14 |
<.0001 |
| 58-65 |
1 |
-0.0600 |
0.0425 |
-0.1433 |
0.0233 |
1.99 |
0.1578 |
| 79-92 |
1 |
-0.0013 |
0.0421 |
-0.0839 |
0.0812 |
0.00 |
0.9749 |
| 93-108 |
1 |
0.1026 |
0.0542 |
-0.0036 |
0.2089 |
3.58 |
0.0584 |
| 66-78 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1031-1094 |
1 |
-0.1483 |
0.0461 |
-0.2387 |
-0.0580 |
10.35 |
0.0013 |
| 1095-1269 |
1 |
-0.1403 |
0.0398 |
-0.2182 |
-0.0624 |
12.45 |
0.0004 |
| 1270-1379 |
1 |
-0.1867 |
0.0596 |
-0.3034 |
-0.0699 |
9.82 |
0.0017 |
| 1380-1424 |
1 |
-0.3746 |
0.1130 |
-0.5960 |
-0.1532 |
10.99 |
0.0009 |
| 1425-1520 |
1 |
-0.0823 |
0.0858 |
-0.2504 |
0.0859 |
0.92 |
0.3376 |
| 1521- |
1 |
0.0122 |
0.1096 |
-0.2025 |
0.2270 |
0.01 |
0.9110 |
| 555-691 |
1 |
-0.0757 |
0.0716 |
-0.2161 |
0.0646 |
1.12 |
0.2904 |
| 692-720 |
1 |
0.0265 |
0.0589 |
-0.0890 |
0.1420 |
0.20 |
0.6534 |
| 721-800 |
1 |
0.0621 |
0.0475 |
-0.0310 |
0.1552 |
1.71 |
0.1910 |
| 801-905 |
1 |
0.0875 |
0.0390 |
0.0112 |
0.1639 |
5.04 |
0.0247 |
| 981-1030 |
1 |
-0.0437 |
0.0395 |
-0.1212 |
0.0337 |
1.23 |
0.2683 |
| 906-980 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.5015 |
0.0330 |
-0.5661 |
-0.4369 |
231.24 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 8 |
518.15 |
<.0001 |
| 13 |
78.41 |
<.0001 |
| 11 |
48.61 |
<.0001 |
| 1 |
213.61 |
<.0001 |
proc genmod data = polizzecum;
class eta(ref='35-43') potkil(ref='66-78') massa(ref='906-980') bendie sesso;
model nsincum = eta potkil massa bendie sesso /
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 9 |
18-22 23-26 27-30 31-34 44-51 52-60 61-69 70- 35-43 |
| 14 |
109-123 124-139 140-143 144-150 151- 17-26 27-33 34-39 40-49 50-57 58-65 79-92 93-108 66-78 |
| 12 |
1031-1094 1095-1269 1270-1379 1380-1424 1425-1520 1521- 555-691 692-720 721-800 801-905 981-1030 906-980 |
| 2 |
B D |
| 2 |
F M |
| 26E3 |
19964.3907 |
0.7616 |
| 26E3 |
19964.3907 |
0.7616 |
| 26E3 |
35140.5681 |
1.3405 |
| 26E3 |
35140.5681 |
1.3405 |
| |
-11312.0005 |
|
| |
-18041.6604 |
|
| |
36153.3209 |
|
| |
36153.4170 |
|
| |
36439.4593 |
|
| |
1 |
-1.8281 |
0.0523 |
-1.9306 |
-1.7256 |
1221.91 |
<.0001 |
| 18-22 |
1 |
0.7886 |
0.0380 |
0.7141 |
0.8630 |
431.18 |
<.0001 |
| 23-26 |
1 |
0.4885 |
0.0341 |
0.4217 |
0.5552 |
205.48 |
<.0001 |
| 27-30 |
1 |
0.2112 |
0.0350 |
0.1426 |
0.2798 |
36.39 |
<.0001 |
| 31-34 |
1 |
0.0929 |
0.0363 |
0.0218 |
0.1640 |
6.55 |
0.0105 |
| 44-51 |
1 |
0.1910 |
0.0310 |
0.1302 |
0.2518 |
37.90 |
<.0001 |
| 52-60 |
1 |
0.2370 |
0.0319 |
0.1745 |
0.2996 |
55.18 |
<.0001 |
| 61-69 |
1 |
0.1138 |
0.0385 |
0.0384 |
0.1893 |
8.75 |
0.0031 |
| 70- |
1 |
0.2266 |
0.0492 |
0.1302 |
0.3230 |
21.21 |
<.0001 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 109-123 |
1 |
-0.0332 |
0.0931 |
-0.2156 |
0.1493 |
0.13 |
0.7215 |
| 124-139 |
1 |
-0.0002 |
0.1437 |
-0.2818 |
0.2815 |
0.00 |
0.9990 |
| 140-143 |
1 |
0.2987 |
0.4098 |
-0.5045 |
1.1019 |
0.53 |
0.4661 |
| 144-150 |
1 |
0.3901 |
0.1742 |
0.0488 |
0.7315 |
5.02 |
0.0251 |
| 151- |
1 |
-0.3132 |
0.1654 |
-0.6373 |
0.0110 |
3.59 |
0.0583 |
| 17-26 |
1 |
-0.3223 |
0.0699 |
-0.4593 |
-0.1852 |
21.25 |
<.0001 |
| 27-33 |
1 |
-0.3164 |
0.0543 |
-0.4228 |
-0.2099 |
33.93 |
<.0001 |
| 34-39 |
1 |
-0.3679 |
0.0583 |
-0.4822 |
-0.2536 |
39.80 |
<.0001 |
| 40-49 |
1 |
-0.2529 |
0.0441 |
-0.3394 |
-0.1664 |
32.84 |
<.0001 |
| 50-57 |
1 |
-0.2145 |
0.0385 |
-0.2899 |
-0.1391 |
31.08 |
<.0001 |
| 58-65 |
1 |
-0.0600 |
0.0425 |
-0.1433 |
0.0233 |
1.99 |
0.1578 |
| 79-92 |
1 |
-0.0014 |
0.0421 |
-0.0840 |
0.0812 |
0.00 |
0.9733 |
| 93-108 |
1 |
0.1024 |
0.0542 |
-0.0038 |
0.2087 |
3.57 |
0.0589 |
| 66-78 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1031-1094 |
1 |
-0.1484 |
0.0461 |
-0.2387 |
-0.0580 |
10.35 |
0.0013 |
| 1095-1269 |
1 |
-0.1403 |
0.0398 |
-0.2182 |
-0.0624 |
12.45 |
0.0004 |
| 1270-1379 |
1 |
-0.1866 |
0.0596 |
-0.3034 |
-0.0698 |
9.81 |
0.0017 |
| 1380-1424 |
1 |
-0.3745 |
0.1130 |
-0.5959 |
-0.1530 |
10.99 |
0.0009 |
| 1425-1520 |
1 |
-0.0821 |
0.0858 |
-0.2502 |
0.0861 |
0.91 |
0.3389 |
| 1521- |
1 |
0.0127 |
0.1096 |
-0.2022 |
0.2275 |
0.01 |
0.9081 |
| 555-691 |
1 |
-0.0751 |
0.0718 |
-0.2158 |
0.0656 |
1.09 |
0.2956 |
| 692-720 |
1 |
0.0269 |
0.0590 |
-0.0888 |
0.1425 |
0.21 |
0.6489 |
| 721-800 |
1 |
0.0625 |
0.0476 |
-0.0308 |
0.1558 |
1.73 |
0.1889 |
| 801-905 |
1 |
0.0877 |
0.0390 |
0.0113 |
0.1641 |
5.06 |
0.0245 |
| 981-1030 |
1 |
-0.0438 |
0.0395 |
-0.1213 |
0.0336 |
1.23 |
0.2676 |
| 906-980 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.5012 |
0.0330 |
-0.5660 |
-0.4365 |
230.12 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| F |
1 |
-0.0028 |
0.0210 |
-0.0441 |
0.0384 |
0.02 |
0.8933 |
| M |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 8 |
518.13 |
<.0001 |
| 13 |
77.83 |
<.0001 |
| 11 |
48.62 |
<.0001 |
| 1 |
212.73 |
<.0001 |
| 1 |
0.02 |
0.8933 |
proc genmod data = polizzecum;
class eta(ref='35-43') potkil(ref='66-78') massa(ref='906-980') bendie capoluogo;
model nsincum = eta potkil massa bendie capoluogo /
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 9 |
18-22 23-26 27-30 31-34 44-51 52-60 61-69 70- 35-43 |
| 14 |
109-123 124-139 140-143 144-150 151- 17-26 27-33 34-39 40-49 50-57 58-65 79-92 93-108 66-78 |
| 12 |
1031-1094 1095-1269 1270-1379 1380-1424 1425-1520 1521- 555-691 692-720 721-800 801-905 981-1030 906-980 |
| 2 |
B D |
| 2 |
NO SI |
| 26E3 |
19721.4813 |
0.7523 |
| 26E3 |
19721.4813 |
0.7523 |
| 26E3 |
32393.3269 |
1.2357 |
| 26E3 |
32393.3269 |
1.2357 |
| |
-11190.5458 |
|
| |
-17920.2058 |
|
| |
35910.4115 |
|
| |
35910.5076 |
|
| |
36196.5499 |
|
| |
1 |
-1.5455 |
0.0550 |
-1.6533 |
-1.4378 |
790.46 |
<.0001 |
| 18-22 |
1 |
0.8086 |
0.0380 |
0.7342 |
0.8831 |
453.17 |
<.0001 |
| 23-26 |
1 |
0.4985 |
0.0341 |
0.4317 |
0.5653 |
213.96 |
<.0001 |
| 27-30 |
1 |
0.2148 |
0.0350 |
0.1462 |
0.2834 |
37.64 |
<.0001 |
| 31-34 |
1 |
0.0922 |
0.0363 |
0.0211 |
0.1634 |
6.46 |
0.0110 |
| 44-51 |
1 |
0.1864 |
0.0310 |
0.1256 |
0.2472 |
36.10 |
<.0001 |
| 52-60 |
1 |
0.2254 |
0.0318 |
0.1630 |
0.2878 |
50.14 |
<.0001 |
| 61-69 |
1 |
0.0937 |
0.0383 |
0.0186 |
0.1687 |
5.98 |
0.0144 |
| 70- |
1 |
0.1927 |
0.0489 |
0.0968 |
0.2886 |
15.52 |
<.0001 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 109-123 |
1 |
-0.0351 |
0.0931 |
-0.2175 |
0.1474 |
0.14 |
0.7063 |
| 124-139 |
1 |
-0.0161 |
0.1437 |
-0.2978 |
0.2656 |
0.01 |
0.9108 |
| 140-143 |
1 |
0.3003 |
0.4098 |
-0.5029 |
1.1035 |
0.54 |
0.4637 |
| 144-150 |
1 |
0.4041 |
0.1742 |
0.0627 |
0.7455 |
5.38 |
0.0203 |
| 151- |
1 |
-0.3249 |
0.1654 |
-0.6492 |
-0.0007 |
3.86 |
0.0495 |
| 17-26 |
1 |
-0.2975 |
0.0697 |
-0.4341 |
-0.1610 |
18.25 |
<.0001 |
| 27-33 |
1 |
-0.3007 |
0.0541 |
-0.4068 |
-0.1946 |
30.84 |
<.0001 |
| 34-39 |
1 |
-0.3507 |
0.0582 |
-0.4647 |
-0.2367 |
36.34 |
<.0001 |
| 40-49 |
1 |
-0.2385 |
0.0440 |
-0.3248 |
-0.1522 |
29.32 |
<.0001 |
| 50-57 |
1 |
-0.2035 |
0.0385 |
-0.2788 |
-0.1281 |
27.99 |
<.0001 |
| 58-65 |
1 |
-0.0572 |
0.0425 |
-0.1404 |
0.0261 |
1.81 |
0.1784 |
| 79-92 |
1 |
-0.0036 |
0.0421 |
-0.0861 |
0.0790 |
0.01 |
0.9327 |
| 93-108 |
1 |
0.1003 |
0.0542 |
-0.0059 |
0.2066 |
3.42 |
0.0643 |
| 66-78 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1031-1094 |
1 |
-0.1421 |
0.0461 |
-0.2325 |
-0.0517 |
9.49 |
0.0021 |
| 1095-1269 |
1 |
-0.1375 |
0.0398 |
-0.2155 |
-0.0596 |
11.96 |
0.0005 |
| 1270-1379 |
1 |
-0.1863 |
0.0596 |
-0.3031 |
-0.0695 |
9.78 |
0.0018 |
| 1380-1424 |
1 |
-0.3823 |
0.1130 |
-0.6037 |
-0.1608 |
11.45 |
0.0007 |
| 1425-1520 |
1 |
-0.0955 |
0.0858 |
-0.2638 |
0.0727 |
1.24 |
0.2659 |
| 1521- |
1 |
0.0133 |
0.1096 |
-0.2016 |
0.2281 |
0.01 |
0.9036 |
| 555-691 |
1 |
-0.0942 |
0.0716 |
-0.2345 |
0.0461 |
1.73 |
0.1881 |
| 692-720 |
1 |
0.0211 |
0.0589 |
-0.0943 |
0.1366 |
0.13 |
0.7198 |
| 721-800 |
1 |
0.0604 |
0.0475 |
-0.0326 |
0.1535 |
1.62 |
0.2030 |
| 801-905 |
1 |
0.0851 |
0.0390 |
0.0088 |
0.1615 |
4.78 |
0.0289 |
| 981-1030 |
1 |
-0.0424 |
0.0395 |
-0.1198 |
0.0350 |
1.15 |
0.2832 |
| 906-980 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.5194 |
0.0330 |
-0.5841 |
-0.4547 |
247.75 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
-0.3422 |
0.0213 |
-0.3839 |
-0.3005 |
258.58 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 8 |
548.11 |
<.0001 |
| 13 |
72.46 |
<.0001 |
| 11 |
48.64 |
<.0001 |
| 1 |
228.22 |
<.0001 |
| 1 |
242.93 |
<.0001 |
ods select contrasts;
proc genmod data = polizzecum;
class eta(ref='35-43') potkil(ref='66-78') massa(ref='906-980') bendie capoluogo prov(ref='prov1');
model nsincum = eta potkil massa bendie capoluogo prov /
dist = poisson
offset = lnespocum
type3;
contrast "eta 61-" eta 0 0 0 0 0 0 1 -1 0;
run;
SAS Output
ods select contrasts;
proc genmod data = polizzecum;
class eta(ref='35-43') potkil(ref='66-78') massa(ref='906-980') bendie capoluogo prov(ref='prov1');
model nsincum = eta potkil massa bendie capoluogo prov /
dist = poisson
offset = lnespocum
type3;
contrast "potkil" potkil 1 -1 0 0 0 0 0 0 0 0 0 0 0 0,
potkil 0 1 -1 0 0 0 0 0 0 0 0 0 0 0,
potkil 0 0 1 -1 0 0 0 0 0 0 0 0 0 0,
potkil 0 0 0 1 -1 0 0 0 0 0 0 0 0 0;
run;
SAS Output
ods select contrasts;
proc genmod data = polizzecum;
class eta(ref='35-43') potkil(ref='66-78') massa(ref='906-980') bendie capoluogo prov(ref='prov1');
model nsincum = eta potkil massa bendie capoluogo prov /
dist = poisson
offset = lnespocum
type3;
contrast "massa" massa 0 0 0 0 0 0 1 -1 0 0 0 0,
massa 0 0 0 0 0 0 0 1 -1 0 0 0,
massa 0 0 0 0 0 0 0 0 1 -1 0 0,
massa 0 0 0 0 0 0 0 0 0 0 1 -1;
run;
SAS Output
proc format;
value classeta
low-22 = "18-22"
23-26 = "23-26"
27-30 = "27-30"
31-34 = "31-34"
35-43 = "35-43"
44-51 = "44-51"
52-60 = "52-60"
61-high = "61-";
run;
proc format;
value classpotkil
low-57 = "-57"
58-high = "58-";
run;
proc format;
value classmassa
low-1030 = "-1030"
1031-1379 = "1031-1379"
1380-1424 = "1380-1424"
1425-high = "1425-";
run;
proc print data = polizze (obs = 10);
run;
SAS Output
| F |
35-43 |
prov8 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
35-43 |
prov5 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44-51 |
prov7 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
18-22 |
prov10 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44-51 |
prov9 |
NO |
B |
-57 |
-1030 |
8-13 |
0.20000 |
0 |
0.000 |
0 |
-1.60944 |
| F |
44-51 |
prov8 |
NO |
B |
-57 |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
35-43 |
prov1 |
NO |
D |
-57 |
1031-1379 |
17-21 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
61- |
prov1 |
SI |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
44-51 |
prov1 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
52-60 |
prov1 |
NO |
B |
58- |
1031-1379 |
17-21 |
1.00000 |
1 |
359.057 |
1 |
0.00000 |
proc genmod data = polizzecum;
class eta(ref='35-43') potkil massa bendie capoluogo prov(ref='prov1');
model nsincum = eta potkil massa bendie capoluogo prov /
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 8 |
18-22 23-26 27-30 31-34 44-51 52-60 61- 35-43 |
| 2 |
-57 58- |
| 4 |
-1030 1031-1379 1380-1424 1425- |
| 2 |
B D |
| 2 |
NO SI |
| 12 |
prov10 prov11 prov12 prov2 prov3 prov4 prov5 prov6 prov7 prov8 prov9 prov1 |
| 26E3 |
19374.9753 |
0.7388 |
| 26E3 |
19374.9753 |
0.7388 |
| 26E3 |
31273.9757 |
1.1926 |
| 26E3 |
31273.9757 |
1.1926 |
| |
-11017.2928 |
|
| |
-17746.9527 |
|
| |
35543.9055 |
|
| |
35543.9550 |
|
| |
35748.2900 |
|
| |
1 |
-1.7699 |
0.0677 |
-1.9027 |
-1.6372 |
682.67 |
<.0001 |
| 18-22 |
1 |
0.8400 |
0.0378 |
0.7660 |
0.9140 |
494.78 |
<.0001 |
| 23-26 |
1 |
0.5168 |
0.0339 |
0.4503 |
0.5833 |
232.00 |
<.0001 |
| 27-30 |
1 |
0.2237 |
0.0350 |
0.1551 |
0.2922 |
40.92 |
<.0001 |
| 31-34 |
1 |
0.0960 |
0.0363 |
0.0249 |
0.1672 |
7.01 |
0.0081 |
| 44-51 |
1 |
0.1825 |
0.0310 |
0.1217 |
0.2433 |
34.64 |
<.0001 |
| 52-60 |
1 |
0.2150 |
0.0318 |
0.1526 |
0.2774 |
45.67 |
<.0001 |
| 61- |
1 |
0.1164 |
0.0336 |
0.0505 |
0.1824 |
11.98 |
0.0005 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.2159 |
0.0259 |
-0.2666 |
-0.1652 |
69.74 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -1030 |
1 |
0.0076 |
0.0647 |
-0.1192 |
0.1345 |
0.01 |
0.9062 |
| 1031-1379 |
1 |
-0.0946 |
0.0612 |
-0.2146 |
0.0253 |
2.39 |
0.1221 |
| 1380-1424 |
1 |
-0.2787 |
0.1190 |
-0.5120 |
-0.0455 |
5.49 |
0.0192 |
| 1425- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.4852 |
0.0303 |
-0.5446 |
-0.4258 |
256.22 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
-0.2836 |
0.0216 |
-0.3260 |
-0.2411 |
171.59 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10 |
1 |
-0.2317 |
0.0485 |
-0.3268 |
-0.1366 |
22.82 |
<.0001 |
| prov11 |
1 |
0.5183 |
0.0475 |
0.4252 |
0.6114 |
119.09 |
<.0001 |
| prov12 |
1 |
-0.4993 |
0.1147 |
-0.7242 |
-0.2745 |
18.95 |
<.0001 |
| prov2 |
1 |
0.3631 |
0.0630 |
0.2397 |
0.4865 |
33.24 |
<.0001 |
| prov3 |
1 |
0.0533 |
0.0364 |
-0.0179 |
0.1246 |
2.15 |
0.1424 |
| prov4 |
1 |
-0.0786 |
0.0338 |
-0.1448 |
-0.0125 |
5.43 |
0.0198 |
| prov5 |
1 |
0.1152 |
0.0335 |
0.0495 |
0.1809 |
11.81 |
0.0006 |
| prov6 |
1 |
0.2006 |
0.0350 |
0.1319 |
0.2692 |
32.78 |
<.0001 |
| prov7 |
1 |
0.2210 |
0.0428 |
0.1371 |
0.3049 |
26.66 |
<.0001 |
| prov8 |
1 |
0.2775 |
0.0313 |
0.2161 |
0.3389 |
78.46 |
<.0001 |
| prov9 |
1 |
0.3905 |
0.0484 |
0.2957 |
0.4854 |
65.18 |
<.0001 |
| prov1 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 7 |
598.63 |
<.0001 |
| 1 |
67.96 |
<.0001 |
| 3 |
18.65 |
0.0003 |
| 1 |
231.49 |
<.0001 |
| 1 |
163.48 |
<.0001 |
| 11 |
403.20 |
<.0001 |
proc genmod data = polizzecum;
class eta(ref='35-43') potkil bendie capoluogo prov(ref='prov1');
model nsincum = eta potkil bendie capoluogo prov /
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 8 |
18-22 23-26 27-30 31-34 44-51 52-60 61- 35-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 12 |
prov10 prov11 prov12 prov2 prov3 prov4 prov5 prov6 prov7 prov8 prov9 prov1 |
| 26E3 |
19393.6287 |
0.7395 |
| 26E3 |
19393.6287 |
0.7395 |
| 26E3 |
31381.2516 |
1.1965 |
| 26E3 |
31381.2516 |
1.1965 |
| |
-11026.6195 |
|
| |
-17756.2794 |
|
| |
35556.5588 |
|
| |
35556.5974 |
|
| |
35736.4173 |
|
| |
1 |
-1.8533 |
0.0439 |
-1.9394 |
-1.7672 |
1780.63 |
<.0001 |
| 18-22 |
1 |
0.8516 |
0.0376 |
0.7778 |
0.9253 |
512.06 |
<.0001 |
| 23-26 |
1 |
0.5255 |
0.0338 |
0.4592 |
0.5918 |
241.26 |
<.0001 |
| 27-30 |
1 |
0.2280 |
0.0349 |
0.1596 |
0.2965 |
42.61 |
<.0001 |
| 31-34 |
1 |
0.0976 |
0.0363 |
0.0265 |
0.1687 |
7.24 |
0.0071 |
| 44-51 |
1 |
0.1832 |
0.0310 |
0.1225 |
0.2440 |
34.93 |
<.0001 |
| 52-60 |
1 |
0.2165 |
0.0318 |
0.1541 |
0.2788 |
46.32 |
<.0001 |
| 61- |
1 |
0.1192 |
0.0336 |
0.0532 |
0.1851 |
12.55 |
0.0004 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.1544 |
0.0190 |
-0.1917 |
-0.1171 |
65.89 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.4639 |
0.0288 |
-0.5204 |
-0.4074 |
258.83 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
-0.2837 |
0.0216 |
-0.3261 |
-0.2413 |
171.79 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10 |
1 |
-0.2306 |
0.0485 |
-0.3256 |
-0.1355 |
22.59 |
<.0001 |
| prov11 |
1 |
0.5229 |
0.0475 |
0.4298 |
0.6159 |
121.32 |
<.0001 |
| prov12 |
1 |
-0.4986 |
0.1147 |
-0.7234 |
-0.2737 |
18.89 |
<.0001 |
| prov2 |
1 |
0.3638 |
0.0630 |
0.2403 |
0.4872 |
33.37 |
<.0001 |
| prov3 |
1 |
0.0527 |
0.0364 |
-0.0186 |
0.1240 |
2.10 |
0.1473 |
| prov4 |
1 |
-0.0784 |
0.0338 |
-0.1445 |
-0.0122 |
5.39 |
0.0202 |
| prov5 |
1 |
0.1160 |
0.0335 |
0.0503 |
0.1817 |
11.97 |
0.0005 |
| prov6 |
1 |
0.2018 |
0.0350 |
0.1332 |
0.2705 |
33.20 |
<.0001 |
| prov7 |
1 |
0.2228 |
0.0428 |
0.1390 |
0.3067 |
27.11 |
<.0001 |
| prov8 |
1 |
0.2798 |
0.0313 |
0.2184 |
0.3412 |
79.82 |
<.0001 |
| prov9 |
1 |
0.3915 |
0.0484 |
0.2967 |
0.4863 |
65.50 |
<.0001 |
| prov1 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 7 |
620.66 |
<.0001 |
| 1 |
64.81 |
<.0001 |
| 1 |
230.93 |
<.0001 |
| 1 |
163.67 |
<.0001 |
| 11 |
407.01 |
<.0001 |
ods select contrasts;
proc genmod data = polizzecum;
class eta(ref='35-43') potkil massa bendie capoluogo prov(ref='prov1');
model nsincum = eta potkil massa bendie capoluogo prov /
dist = poisson
offset = lnespocum
type3;
contrast "province" prov 1 0 -1 0 0 0 0 0 0 0 0 0,
prov 0 0 0 1 0 0 0 0 0 0 -1 0,
prov 0 0 0 0 1 0 0 0 0 0 0 -1;
run;
SAS Output
proc format;
value $classprov
"RC","VT","CN","OR","RA","VC","FE","LC","SS","VV","BZ","PV","RG","CH","PG","AR","TE","TN","VR","EN","NO","SV","VI","MC","MT","RE","BS","RI","AG","AV","PC" = "prov1-3"
"BN","PO","IM","BA","PT","TA","SP","CA","ROMA","PA" = "prov2-9"
"AL","SO","GO","LT","PR","PN","GR","UD","TV","PD" = "prov4"
"SI","TR","AP","LO","FG","ME","LU","CZ","FR","CT","VE","BG","IS","MO","TP" = "prov5"
"CL","PI","VA","BR","FO","LI","SR","CO","SA" = "prov6"
"LE","RN","AN","MS","BO","GE","TS" = "prov7"
"CB","FI","NU","PE","TO","MI" = "prov8"
"BL","PZ","BI","CR","CS","AT","MN","PS","AQ","RSM","VB","RO" = "prov10-12"
"AO","NA","CE","KR" = "prov11";
run;
proc print data = polizze (obs = 10);
run;
SAS Output
| F |
35-43 |
prov8 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
35-43 |
prov5 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44-51 |
prov7 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
18-22 |
prov10-12 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44-51 |
prov2-9 |
NO |
B |
-57 |
-1030 |
8-13 |
0.20000 |
0 |
0.000 |
0 |
-1.60944 |
| F |
44-51 |
prov8 |
NO |
B |
-57 |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
35-43 |
prov1-3 |
NO |
D |
-57 |
1031-1379 |
17-21 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
61- |
prov1-3 |
SI |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
44-51 |
prov1-3 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
52-60 |
prov1-3 |
NO |
B |
58- |
1031-1379 |
17-21 |
1.00000 |
1 |
359.057 |
1 |
0.00000 |
proc genmod data = polizzecum plots = stdreschi;
class eta(ref='35-43') potkil bendie capoluogo prov(ref='prov1-3');
model nsincum = eta potkil bendie capoluogo prov /
dist = poisson
offset = lnespocum
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 8 |
18-22 23-26 27-30 31-34 44-51 52-60 61- 35-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 9 |
prov10-12 prov11 prov2-9 prov4 prov5 prov6 prov7 prov8 prov1-3 |
| 26E3 |
19401.1531 |
0.7397 |
| 26E3 |
19401.1531 |
0.7397 |
| 26E3 |
31341.9422 |
1.1949 |
| 26E3 |
31341.9422 |
1.1949 |
| |
-11030.3817 |
|
| |
-17760.0417 |
|
| |
35558.0833 |
|
| |
35558.1123 |
|
| |
35713.4156 |
|
| |
1 |
-1.8338 |
0.0417 |
-1.9156 |
-1.7520 |
1930.62 |
<.0001 |
| 18-22 |
1 |
0.8517 |
0.0376 |
0.7780 |
0.9255 |
512.26 |
<.0001 |
| 23-26 |
1 |
0.5256 |
0.0338 |
0.4593 |
0.5919 |
241.34 |
<.0001 |
| 27-30 |
1 |
0.2280 |
0.0349 |
0.1595 |
0.2964 |
42.58 |
<.0001 |
| 31-34 |
1 |
0.0974 |
0.0363 |
0.0263 |
0.1685 |
7.22 |
0.0072 |
| 44-51 |
1 |
0.1833 |
0.0310 |
0.1225 |
0.2440 |
34.94 |
<.0001 |
| 52-60 |
1 |
0.2171 |
0.0318 |
0.1547 |
0.2794 |
46.57 |
<.0001 |
| 61- |
1 |
0.1193 |
0.0336 |
0.0533 |
0.1852 |
12.57 |
0.0004 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.1546 |
0.0190 |
-0.1919 |
-0.1173 |
66.05 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.4636 |
0.0288 |
-0.5201 |
-0.4071 |
258.53 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
-0.2839 |
0.0216 |
-0.3263 |
-0.2416 |
172.74 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10-12 |
1 |
-0.2886 |
0.0439 |
-0.3747 |
-0.2025 |
43.21 |
<.0001 |
| prov11 |
1 |
0.5033 |
0.0455 |
0.4142 |
0.5924 |
122.63 |
<.0001 |
| prov2-9 |
1 |
0.3623 |
0.0389 |
0.2860 |
0.4385 |
86.64 |
<.0001 |
| prov4 |
1 |
-0.0980 |
0.0308 |
-0.1584 |
-0.0375 |
10.09 |
0.0015 |
| prov5 |
1 |
0.0964 |
0.0306 |
0.0365 |
0.1563 |
9.94 |
0.0016 |
| prov6 |
1 |
0.1822 |
0.0322 |
0.1191 |
0.2454 |
31.99 |
<.0001 |
| prov7 |
1 |
0.2032 |
0.0405 |
0.1238 |
0.2827 |
25.13 |
<.0001 |
| prov8 |
1 |
0.2602 |
0.0281 |
0.2050 |
0.3154 |
85.46 |
<.0001 |
| prov1-3 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 7 |
620.90 |
<.0001 |
| 1 |
64.97 |
<.0001 |
| 1 |
230.67 |
<.0001 |
| 1 |
164.52 |
<.0001 |
| 8 |
399.48 |
<.0001 |
proc genmod data = polizzecum plots = stdreschi(xbeta);
class eta(ref='35-43') potkil bendie capoluogo prov(ref='prov1-3');
model nsincum = eta potkil bendie capoluogo prov /
dist = poisson
offset = lnespocum;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 8 |
18-22 23-26 27-30 31-34 44-51 52-60 61- 35-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 9 |
prov10-12 prov11 prov2-9 prov4 prov5 prov6 prov7 prov8 prov1-3 |
| 26E3 |
19401.1531 |
0.7397 |
| 26E3 |
19401.1531 |
0.7397 |
| 26E3 |
31341.9422 |
1.1949 |
| 26E3 |
31341.9422 |
1.1949 |
| |
-11030.3817 |
|
| |
-17760.0417 |
|
| |
35558.0833 |
|
| |
35558.1123 |
|
| |
35713.4156 |
|
| |
1 |
-1.8338 |
0.0417 |
-1.9156 |
-1.7520 |
1930.62 |
<.0001 |
| 18-22 |
1 |
0.8517 |
0.0376 |
0.7780 |
0.9255 |
512.26 |
<.0001 |
| 23-26 |
1 |
0.5256 |
0.0338 |
0.4593 |
0.5919 |
241.34 |
<.0001 |
| 27-30 |
1 |
0.2280 |
0.0349 |
0.1595 |
0.2964 |
42.58 |
<.0001 |
| 31-34 |
1 |
0.0974 |
0.0363 |
0.0263 |
0.1685 |
7.22 |
0.0072 |
| 44-51 |
1 |
0.1833 |
0.0310 |
0.1225 |
0.2440 |
34.94 |
<.0001 |
| 52-60 |
1 |
0.2171 |
0.0318 |
0.1547 |
0.2794 |
46.57 |
<.0001 |
| 61- |
1 |
0.1193 |
0.0336 |
0.0533 |
0.1852 |
12.57 |
0.0004 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.1546 |
0.0190 |
-0.1919 |
-0.1173 |
66.05 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.4636 |
0.0288 |
-0.5201 |
-0.4071 |
258.53 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
-0.2839 |
0.0216 |
-0.3263 |
-0.2416 |
172.74 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10-12 |
1 |
-0.2886 |
0.0439 |
-0.3747 |
-0.2025 |
43.21 |
<.0001 |
| prov11 |
1 |
0.5033 |
0.0455 |
0.4142 |
0.5924 |
122.63 |
<.0001 |
| prov2-9 |
1 |
0.3623 |
0.0389 |
0.2860 |
0.4385 |
86.64 |
<.0001 |
| prov4 |
1 |
-0.0980 |
0.0308 |
-0.1584 |
-0.0375 |
10.09 |
0.0015 |
| prov5 |
1 |
0.0964 |
0.0306 |
0.0365 |
0.1563 |
9.94 |
0.0016 |
| prov6 |
1 |
0.1822 |
0.0322 |
0.1191 |
0.2454 |
31.99 |
<.0001 |
| prov7 |
1 |
0.2032 |
0.0405 |
0.1238 |
0.2827 |
25.13 |
<.0001 |
| prov8 |
1 |
0.2602 |
0.0281 |
0.2050 |
0.3154 |
85.46 |
<.0001 |
| prov1-3 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
3.A.1.2 Modello di Poisson con sovradispersione
proc genmod data = polizzecum;
class eta(ref='35-43') potkil bendie capoluogo prov(ref='prov1-3');
model nsincum = eta potkil bendie capoluogo prov /
dist = poisson
offset = lnespocum
scale = pearson
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 8 |
18-22 23-26 27-30 31-34 44-51 52-60 61- 35-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 9 |
prov10-12 prov11 prov2-9 prov4 prov5 prov6 prov7 prov8 prov1-3 |
| 26E3 |
19401.1531 |
0.7397 |
| 26E3 |
16236.7808 |
0.6190 |
| 26E3 |
31341.9422 |
1.1949 |
| 26E3 |
26230.0000 |
1.0000 |
| |
-9231.3013 |
|
| |
-17760.0417 |
|
| |
35558.0833 |
|
| |
35558.1123 |
|
| |
35713.4156 |
|
| |
1 |
-1.8338 |
0.0456 |
-1.9233 |
-1.7444 |
1615.73 |
<.0001 |
| 18-22 |
1 |
0.8517 |
0.0411 |
0.7711 |
0.9323 |
428.71 |
<.0001 |
| 23-26 |
1 |
0.5256 |
0.0370 |
0.4531 |
0.5981 |
201.98 |
<.0001 |
| 27-30 |
1 |
0.2280 |
0.0382 |
0.1531 |
0.3028 |
35.63 |
<.0001 |
| 31-34 |
1 |
0.0974 |
0.0397 |
0.0197 |
0.1752 |
6.04 |
0.0140 |
| 44-51 |
1 |
0.1833 |
0.0339 |
0.1169 |
0.2497 |
29.24 |
<.0001 |
| 52-60 |
1 |
0.2171 |
0.0348 |
0.1489 |
0.2852 |
38.97 |
<.0001 |
| 61- |
1 |
0.1193 |
0.0368 |
0.0472 |
0.1913 |
10.52 |
0.0012 |
| 35-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.1546 |
0.0208 |
-0.1953 |
-0.1138 |
55.28 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.4636 |
0.0315 |
-0.5254 |
-0.4018 |
216.36 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
-0.2839 |
0.0236 |
-0.3302 |
-0.2376 |
144.56 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10-12 |
1 |
-0.2886 |
0.0480 |
-0.3827 |
-0.1945 |
36.16 |
<.0001 |
| prov11 |
1 |
0.5033 |
0.0497 |
0.4059 |
0.6007 |
102.63 |
<.0001 |
| prov2-9 |
1 |
0.3623 |
0.0425 |
0.2789 |
0.4456 |
72.51 |
<.0001 |
| prov4 |
1 |
-0.0980 |
0.0337 |
-0.1640 |
-0.0319 |
8.45 |
0.0037 |
| prov5 |
1 |
0.0964 |
0.0334 |
0.0309 |
0.1619 |
8.32 |
0.0039 |
| prov6 |
1 |
0.1822 |
0.0352 |
0.1132 |
0.2513 |
26.77 |
<.0001 |
| prov7 |
1 |
0.2032 |
0.0443 |
0.1164 |
0.2901 |
21.03 |
<.0001 |
| prov8 |
1 |
0.2602 |
0.0308 |
0.1999 |
0.3205 |
71.52 |
<.0001 |
| prov1-3 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0931 |
0.0000 |
1.0931 |
1.0931 |
|
|
Note:The scale parameter was estimated by the square root of Pearson's Chi-Square/DOF.
| 7 |
26230 |
74.23 |
<.0001 |
519.63 |
<.0001 |
| 1 |
26230 |
54.38 |
<.0001 |
54.38 |
<.0001 |
| 1 |
26230 |
193.05 |
<.0001 |
193.05 |
<.0001 |
| 1 |
26230 |
137.69 |
<.0001 |
137.69 |
<.0001 |
| 8 |
26230 |
41.79 |
<.0001 |
334.33 |
<.0001 |
ods select contrasts;
proc genmod data = polizzecum;
class eta(ref='35-43') potkil bendie capoluogo prov(ref='prov1-3');
model nsincum = eta potkil bendie capoluogo prov /
dist = poisson
offset = lnespocum
scale = pearson
type3;
contrast "eta" eta 0 0 0 1 0 0 0 -1;
run;
SAS Output
| 1 |
26230 |
5.98 |
0.0145 |
5.98 |
0.0145 |
LR |
proc format;
value classeta
low-22 = "18-22"
23-26 = "23-26"
27-30 = "27-30"
31-43 = "31-43"
44-51 = "44-51"
52-60 = "52-60"
61-high = "61-";
run;
proc print data = polizze (obs = 10);
run;
SAS Output
| F |
31-43 |
prov8 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
31-43 |
prov5 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44-51 |
prov7 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
18-22 |
prov10-12 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44-51 |
prov2-9 |
NO |
B |
-57 |
-1030 |
8-13 |
0.20000 |
0 |
0.000 |
0 |
-1.60944 |
| F |
44-51 |
prov8 |
NO |
B |
-57 |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
31-43 |
prov1-3 |
NO |
D |
-57 |
1031-1379 |
17-21 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
61- |
prov1-3 |
SI |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
44-51 |
prov1-3 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
52-60 |
prov1-3 |
NO |
B |
58- |
1031-1379 |
17-21 |
1.00000 |
1 |
359.057 |
1 |
0.00000 |
proc genmod data = polizzecum plots = stdreschi(xbeta);
class eta(ref='31-43') potkil bendie capoluogo prov(ref='prov1-3');
model nsincum = eta potkil bendie capoluogo prov /
dist = poisson
offset = lnespocum
scale = pearson
type3;
run;
SAS Output
| WORK.POLIZZECUM |
| Poisson |
| Log |
| nsincum |
| lnespocum |
| 7 |
18-22 23-26 27-30 44-51 52-60 61- 31-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 9 |
prov10-12 prov11 prov2-9 prov4 prov5 prov6 prov7 prov8 prov1-3 |
| 26E3 |
19408.3010 |
0.7399 |
| 26E3 |
16187.7678 |
0.6171 |
| 26E3 |
31449.6198 |
1.1989 |
| 26E3 |
26231.0000 |
1.0000 |
| |
-9203.0267 |
|
| |
-17763.6156 |
|
| |
35563.2312 |
|
| |
35563.2573 |
|
| |
35710.3881 |
|
| |
1 |
-1.7995 |
0.0434 |
-1.8845 |
-1.7145 |
1722.27 |
<.0001 |
| 18-22 |
1 |
0.8176 |
0.0386 |
0.7419 |
0.8933 |
448.06 |
<.0001 |
| 23-26 |
1 |
0.4915 |
0.0342 |
0.4245 |
0.5584 |
207.06 |
<.0001 |
| 27-30 |
1 |
0.1939 |
0.0355 |
0.1244 |
0.2634 |
29.88 |
<.0001 |
| 44-51 |
1 |
0.1492 |
0.0308 |
0.0889 |
0.2095 |
23.50 |
<.0001 |
| 52-60 |
1 |
0.1830 |
0.0317 |
0.1208 |
0.2452 |
33.23 |
<.0001 |
| 61- |
1 |
0.0852 |
0.0339 |
0.0187 |
0.1517 |
6.31 |
0.0120 |
| 31-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.1541 |
0.0208 |
-0.1950 |
-0.1133 |
54.76 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.4640 |
0.0316 |
-0.5259 |
-0.4021 |
216.03 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
-0.2840 |
0.0237 |
-0.3304 |
-0.2377 |
144.18 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10-12 |
1 |
-0.2889 |
0.0481 |
-0.3832 |
-0.1947 |
36.12 |
<.0001 |
| prov11 |
1 |
0.5036 |
0.0498 |
0.4060 |
0.6011 |
102.38 |
<.0001 |
| prov2-9 |
1 |
0.3622 |
0.0426 |
0.2787 |
0.4457 |
72.24 |
<.0001 |
| prov4 |
1 |
-0.0977 |
0.0338 |
-0.1639 |
-0.0315 |
8.38 |
0.0038 |
| prov5 |
1 |
0.0963 |
0.0335 |
0.0307 |
0.1619 |
8.27 |
0.0040 |
| prov6 |
1 |
0.1819 |
0.0353 |
0.1128 |
0.2511 |
26.59 |
<.0001 |
| prov7 |
1 |
0.2030 |
0.0444 |
0.1160 |
0.2900 |
20.92 |
<.0001 |
| prov8 |
1 |
0.2598 |
0.0308 |
0.1994 |
0.3202 |
71.08 |
<.0001 |
| prov1-3 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0950 |
0.0000 |
1.0950 |
1.0950 |
|
|
Note:The scale parameter was estimated by the square root of Pearson's Chi-Square/DOF.
| 6 |
26231 |
85.32 |
<.0001 |
511.91 |
<.0001 |
| 1 |
26231 |
53.87 |
<.0001 |
53.87 |
<.0001 |
| 1 |
26231 |
192.73 |
<.0001 |
192.73 |
<.0001 |
| 1 |
26231 |
137.32 |
<.0001 |
137.32 |
<.0001 |
| 8 |
26231 |
41.63 |
<.0001 |
333.02 |
<.0001 |
3.A.1.3 Modello Binomiale Negativa
proc print data = polizze (obs = 10);
run;
SAS Output
| F |
31-43 |
prov8 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
31-43 |
prov5 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44-51 |
prov7 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
18-22 |
prov10-12 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44-51 |
prov2-9 |
NO |
B |
-57 |
-1030 |
8-13 |
0.20000 |
0 |
0.000 |
0 |
-1.60944 |
| F |
44-51 |
prov8 |
NO |
B |
-57 |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
31-43 |
prov1-3 |
NO |
D |
-57 |
1031-1379 |
17-21 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
61- |
prov1-3 |
SI |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
44-51 |
prov1-3 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
52-60 |
prov1-3 |
NO |
B |
58- |
1031-1379 |
17-21 |
1.00000 |
1 |
359.057 |
1 |
0.00000 |
ods select ModelInfo;
proc genmod data = polizze;
output out = stime pred = nsinatt;
class eta(ref='31-43') potkil bendie capoluogo prov(ref='prov1-3');
model nsin = eta potkil bendie capoluogo prov /
dist = poisson
offset = lnespo;
run;
SAS Output
| WORK.POLIZZE |
| Poisson |
| Log |
| nsin |
| lnespo |
proc print data = stime (obs = 10);
run;
SAS Output
| F |
31-43 |
prov8 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
0.08700 |
| M |
31-43 |
prov5 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
0.07387 |
| M |
44-51 |
prov7 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
0.11133 |
| F |
18-22 |
prov10-12 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
0.11383 |
| M |
44-51 |
prov2-9 |
NO |
B |
-57 |
-1030 |
8-13 |
0.20000 |
0 |
0.000 |
0 |
-1.60944 |
0.02238 |
| F |
44-51 |
prov8 |
NO |
B |
-57 |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
0.10100 |
| M |
31-43 |
prov1-3 |
NO |
D |
-57 |
1031-1379 |
17-21 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
0.10671 |
| M |
61- |
prov1-3 |
SI |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
0.11323 |
| F |
44-51 |
prov1-3 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
0.09087 |
| M |
52-60 |
prov1-3 |
NO |
B |
58- |
1031-1379 |
17-21 |
1.00000 |
1 |
359.057 |
1 |
0.00000 |
0.09399 |
data alpha_dataset;
set stime;
add = ((nsin - nsinatt)
alphanum = nsinatt
alphaden = (nsin - nsinatt)
keep nsincum nsinatt add alphanum alphaden;
run;
proc means data = alpha_dataset;
var add alphanum alphaden;
output out = alpha_sum sum = sadd salphanum salphaden;
run;
proc print data = alpha_sum (obs = 10);
run;
SAS Output
|
|
|
37.9694385
0.0073439
0.0057876
|
14556.53
0.0087395
0.3862777
|
-6631.66
2.273133E-8
-0.3115638
|
5431253.23
0.2822487
23.8076966
|
| 0 |
172161 |
6536856.50 |
1264.34 |
996.392 |
data alpha;
set alpha_sum;
alpha_ct = (sadd / (_FREQ_ - 17))
alpha_pinquet = salphanum / salphaden;
keep alpha_ct alpha_pinquet;
run;
proc print data = alpha noobs;
run;
SAS Output
proc genmod data = polizze plots = stdreschi(xbeta);
class eta(ref='31-43') potkil bendie capoluogo prov(ref='prov1-3');
alpha = 1.26892;
mu = _MEAN_;
y = _RESP_;
variance var = mu + mu
if y > 0 then
d = 2
else if y = 0 then
d = 2
deviance dev = d;
model nsin = eta potkil bendie capoluogo prov /
link = log
offset = lnespo;
run;
SAS Output
| WORK.POLIZZE |
| User |
| Log |
| nsin |
| lnespo |
| 7 |
18-22 23-26 27-30 44-51 52-60 61- 31-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 9 |
prov10-12 prov11 prov2-9 prov4 prov5 prov6 prov7 prov8 prov1-3 |
| 17E4 |
57559.8543 |
0.3344 |
| 17E4 |
57559.8543 |
0.3344 |
| 17E4 |
192330.8433 |
1.1173 |
| 17E4 |
192330.8433 |
1.1173 |
| |
-28779.9272 |
|
| |
-28779.9272 |
|
| |
57595.8543 |
|
| |
57595.8583 |
|
| |
57776.8657 |
|
| |
1 |
-1.7930 |
0.0414 |
-1.8741 |
-1.7118 |
1875.28 |
<.0001 |
| 18-22 |
1 |
0.8233 |
0.0371 |
0.7506 |
0.8961 |
491.88 |
<.0001 |
| 23-26 |
1 |
0.4948 |
0.0325 |
0.4311 |
0.5585 |
231.65 |
<.0001 |
| 27-30 |
1 |
0.1941 |
0.0335 |
0.1284 |
0.2597 |
33.54 |
<.0001 |
| 44-51 |
1 |
0.1499 |
0.0291 |
0.0930 |
0.2069 |
26.60 |
<.0001 |
| 52-60 |
1 |
0.1853 |
0.0300 |
0.1265 |
0.2441 |
38.11 |
<.0001 |
| 61- |
1 |
0.0856 |
0.0320 |
0.0229 |
0.1483 |
7.16 |
0.0075 |
| 31-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.1558 |
0.0197 |
-0.1945 |
-0.1171 |
62.26 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.4677 |
0.0303 |
-0.5271 |
-0.4082 |
237.71 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
-0.2854 |
0.0225 |
-0.3296 |
-0.2413 |
160.48 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10-12 |
1 |
-0.2901 |
0.0451 |
-0.3784 |
-0.2017 |
41.38 |
<.0001 |
| prov11 |
1 |
0.5074 |
0.0480 |
0.4134 |
0.6014 |
111.95 |
<.0001 |
| prov2-9 |
1 |
0.3674 |
0.0407 |
0.2877 |
0.4472 |
81.54 |
<.0001 |
| prov4 |
1 |
-0.0976 |
0.0318 |
-0.1599 |
-0.0352 |
9.40 |
0.0022 |
| prov5 |
1 |
0.0974 |
0.0317 |
0.0353 |
0.1595 |
9.44 |
0.0021 |
| prov6 |
1 |
0.1827 |
0.0334 |
0.1172 |
0.2483 |
29.87 |
<.0001 |
| prov7 |
1 |
0.2034 |
0.0422 |
0.1208 |
0.2860 |
23.28 |
<.0001 |
| prov8 |
1 |
0.2596 |
0.0292 |
0.2023 |
0.3169 |
78.90 |
<.0001 |
| prov1-3 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
proc genmod data = polizze plots = stdreschi(xbeta);
class eta(ref='31-43') potkil bendie capoluogo prov(ref='prov1-3');
model nsin = eta potkil bendie capoluogo prov /
dist = negbin
link = log
offset = lnespo;
run;
SAS Output
| WORK.POLIZZE |
| Negative Binomial |
| Log |
| nsin |
| lnespo |
| 7 |
18-22 23-26 27-30 44-51 52-60 61- 31-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 9 |
prov10-12 prov11 prov2-9 prov4 prov5 prov6 prov7 prov8 prov1-3 |
| 17E4 |
57409.2051 |
0.3335 |
| 17E4 |
57409.2051 |
0.3335 |
| 17E4 |
192096.0927 |
1.1159 |
| 17E4 |
192096.0927 |
1.1159 |
| |
-44017.1675 |
|
| |
-44721.6472 |
|
| |
89481.2943 |
|
| |
89481.2987 |
|
| |
89672.3618 |
|
| |
1 |
-1.7928 |
0.0414 |
-1.8741 |
-1.7116 |
1871.02 |
<.0001 |
| 18-22 |
1 |
0.8235 |
0.0372 |
0.7506 |
0.8963 |
490.85 |
<.0001 |
| 23-26 |
1 |
0.4949 |
0.0325 |
0.4311 |
0.5586 |
231.28 |
<.0001 |
| 27-30 |
1 |
0.1941 |
0.0335 |
0.1283 |
0.2598 |
33.49 |
<.0001 |
| 44-51 |
1 |
0.1499 |
0.0291 |
0.0929 |
0.2070 |
26.56 |
<.0001 |
| 52-60 |
1 |
0.1853 |
0.0300 |
0.1265 |
0.2442 |
38.07 |
<.0001 |
| 61- |
1 |
0.0856 |
0.0320 |
0.0228 |
0.1484 |
7.15 |
0.0075 |
| 31-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.1559 |
0.0198 |
-0.1946 |
-0.1171 |
62.18 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
-0.4677 |
0.0304 |
-0.5273 |
-0.4082 |
237.23 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
-0.2854 |
0.0226 |
-0.3296 |
-0.2412 |
160.21 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10-12 |
1 |
-0.2901 |
0.0451 |
-0.3785 |
-0.2017 |
41.34 |
<.0001 |
| prov11 |
1 |
0.5075 |
0.0480 |
0.4134 |
0.6016 |
111.71 |
<.0001 |
| prov2-9 |
1 |
0.3676 |
0.0407 |
0.2877 |
0.4474 |
81.42 |
<.0001 |
| prov4 |
1 |
-0.0975 |
0.0318 |
-0.1600 |
-0.0351 |
9.38 |
0.0022 |
| prov5 |
1 |
0.0974 |
0.0317 |
0.0352 |
0.1596 |
9.43 |
0.0021 |
| prov6 |
1 |
0.1827 |
0.0335 |
0.1171 |
0.2483 |
29.82 |
<.0001 |
| prov7 |
1 |
0.2034 |
0.0422 |
0.1207 |
0.2861 |
23.24 |
<.0001 |
| prov8 |
1 |
0.2596 |
0.0293 |
0.2023 |
0.3169 |
78.76 |
<.0001 |
| prov1-3 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
1 |
0.8069 |
0.0589 |
0.6993 |
0.9310 |
|
|
Note:The negative binomial dispersion parameter was estimated by maximum likelihood.
3.A.2 Modelli per il danno per sinistro
Preparazione dei dati
data danni;
set dati.danni;
run;
proc print data = danni (obs = 10);
run;
SAS Output
| M |
55 |
AR |
NO |
B |
80 |
1180 |
18 |
359.06 |
| M |
56 |
TE |
NO |
B |
55 |
1120 |
17 |
1617.55 |
| F |
33 |
VC |
NO |
B |
36 |
795 |
14 |
179.53 |
| F |
56 |
BL |
NO |
B |
66 |
1050 |
17 |
691.19 |
| M |
73 |
MS |
NO |
B |
36 |
765 |
13 |
1617.55 |
| M |
61 |
VI |
NO |
B |
77 |
1200 |
18 |
1201.05 |
| F |
31 |
BA |
NO |
B |
52 |
990 |
15 |
538.59 |
| M |
37 |
VR |
NO |
B |
103 |
1420 |
20 |
359.06 |
| F |
53 |
FO |
NO |
B |
25 |
700 |
10 |
6059.09 |
| M |
70 |
FI |
NO |
B |
65 |
1010 |
17 |
771.97 |
data danni;
set danni;
format prov $classprov.;
format eta classeta.;
format potf classpotf.;
format potkil classpotkil.;
format massa classmassa.;
run;
proc print data = danni (obs = 10);
run;
SAS Output
| M |
52-60 |
prov1-3 |
NO |
B |
58- |
1031-1379 |
17-21 |
359.06 |
| M |
52-60 |
prov1-3 |
NO |
B |
-57 |
1031-1379 |
17-21 |
1617.55 |
| F |
31-43 |
prov1-3 |
NO |
B |
-57 |
-1030 |
14-15 |
179.53 |
| F |
52-60 |
prov10-12 |
NO |
B |
58- |
1031-1379 |
17-21 |
691.19 |
| M |
61- |
prov7 |
NO |
B |
-57 |
-1030 |
8-13 |
1617.55 |
| M |
61- |
prov1-3 |
NO |
B |
58- |
1031-1379 |
17-21 |
1201.05 |
| F |
31-43 |
prov2-9 |
NO |
B |
-57 |
-1030 |
14-15 |
538.59 |
| M |
31-43 |
prov1-3 |
NO |
B |
58- |
1380-1424 |
17-21 |
359.06 |
| F |
52-60 |
prov6 |
NO |
B |
-57 |
-1030 |
8-13 |
6059.09 |
| M |
61- |
prov8 |
NO |
B |
58- |
-1030 |
17-21 |
771.97 |
proc means data = danni nway noprint;
class sesso capoluogo bendie prov eta potf potkil massa;
var danno;
output out = dannicum sum = dannocum;
run;
data dannicum;
set dannicum;
dannocummed = dannocum / _FREQ_;
rename _FREQ_ = nsin;
drop _TYPE_;
run;
proc print data = dannicum (obs = 10);
run;
SAS Output
| F |
NO |
B |
prov1-3 |
18-22 |
8-13 |
-57 |
-1030 |
46 |
128088.48 |
2784.53 |
| F |
NO |
B |
prov1-3 |
18-22 |
8-13 |
58- |
-1030 |
1 |
987.41 |
987.41 |
| F |
NO |
B |
prov1-3 |
18-22 |
14-15 |
-57 |
-1030 |
16 |
54461.79 |
3403.86 |
| F |
NO |
B |
prov1-3 |
18-22 |
14-15 |
58- |
-1030 |
2 |
2441.95 |
1220.97 |
| F |
NO |
B |
prov1-3 |
18-22 |
16 |
-57 |
-1030 |
2 |
4372.42 |
2186.21 |
| F |
NO |
B |
prov1-3 |
18-22 |
16 |
58- |
-1030 |
1 |
10322.89 |
10322.89 |
| F |
NO |
B |
prov1-3 |
18-22 |
17-21 |
-57 |
1031-1379 |
1 |
556.54 |
556.54 |
| F |
NO |
B |
prov1-3 |
18-22 |
17-21 |
58- |
1031-1379 |
2 |
3551.08 |
1775.54 |
| F |
NO |
B |
prov1-3 |
23-26 |
8-13 |
-57 |
-1030 |
62 |
151011.33 |
2435.67 |
| F |
NO |
B |
prov1-3 |
23-26 |
14-15 |
-57 |
-1030 |
26 |
33844.04 |
1301.69 |
proc summary data = dannicum;
output out = conta_righe;
run;
proc print data = conta_righe;
run;
SAS Output
3.A.2.1 Modello Gamma
proc genmod data = danni;
class eta(ref='31-43') potkil bendie capoluogo prov(ref='prov1-3');
model danno = eta potkil bendie capoluogo prov /
dist = gamma
link = log
type3;
run;
SAS Output
| WORK.DANNI |
| Gamma |
| Log |
| danno |
| 7 |
18-22 23-26 27-30 44-51 52-60 61- 31-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 9 |
prov10-12 prov11 prov2-9 prov4 prov5 prov6 prov7 prov8 prov1-3 |
| 13E3 |
17803.3419 |
1.4048 |
| 13E3 |
14967.0467 |
1.1810 |
| 13E3 |
114315.2165 |
9.0204 |
| 13E3 |
96103.3714 |
7.5833 |
| |
-113894.6875 |
|
| |
-113894.6875 |
|
| |
227827.3751 |
|
| |
227827.4350 |
|
| |
227968.8994 |
|
| |
1 |
7.8570 |
0.0436 |
7.7715 |
7.9425 |
32459.9 |
<.0001 |
| 18-22 |
1 |
0.2319 |
0.0386 |
0.1563 |
0.3075 |
36.13 |
<.0001 |
| 23-26 |
1 |
0.1630 |
0.0341 |
0.0961 |
0.2299 |
22.82 |
<.0001 |
| 27-30 |
1 |
0.1060 |
0.0355 |
0.0364 |
0.1757 |
8.90 |
0.0028 |
| 44-51 |
1 |
-0.1213 |
0.0307 |
-0.1815 |
-0.0610 |
15.57 |
<.0001 |
| 52-60 |
1 |
-0.0216 |
0.0317 |
-0.0838 |
0.0405 |
0.47 |
0.4950 |
| 61- |
1 |
-0.0662 |
0.0341 |
-0.1329 |
0.0006 |
3.77 |
0.0522 |
| 31-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.2019 |
0.0208 |
-0.2427 |
-0.1611 |
94.08 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
0.1309 |
0.0315 |
0.0691 |
0.1927 |
17.24 |
<.0001 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
0.1143 |
0.0237 |
0.0678 |
0.1607 |
23.23 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10-12 |
1 |
0.2506 |
0.0480 |
0.1565 |
0.3446 |
27.25 |
<.0001 |
| prov11 |
1 |
-0.2226 |
0.0502 |
-0.3209 |
-0.1243 |
19.68 |
<.0001 |
| prov2-9 |
1 |
-0.1788 |
0.0427 |
-0.2625 |
-0.0951 |
17.54 |
<.0001 |
| prov4 |
1 |
0.1136 |
0.0337 |
0.0476 |
0.1796 |
11.37 |
0.0007 |
| prov5 |
1 |
0.1024 |
0.0335 |
0.0368 |
0.1680 |
9.35 |
0.0022 |
| prov6 |
1 |
0.2153 |
0.0354 |
0.1460 |
0.2846 |
37.09 |
<.0001 |
| prov7 |
1 |
0.0076 |
0.0443 |
-0.0792 |
0.0944 |
0.03 |
0.8633 |
| prov8 |
1 |
-0.0222 |
0.0308 |
-0.0826 |
0.0382 |
0.52 |
0.4713 |
| prov1-3 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
1 |
0.8407 |
0.0091 |
0.8229 |
0.8588 |
|
|
Note:The scale parameter was estimated by maximum likelihood.
| 6 |
123.98 |
<.0001 |
| 1 |
95.58 |
<.0001 |
| 1 |
16.69 |
<.0001 |
| 1 |
22.78 |
<.0001 |
| 8 |
141.13 |
<.0001 |
proc genmod data = dannicum;
class eta(ref='31-43') potkil bendie capoluogo prov(ref='prov1-3');
model dannocummed = eta potkil bendie capoluogo prov /
dist = gamma
link = log
type3;
weight nsin;
run;
SAS Output
| WORK.DANNICUM |
| Gamma |
| Log |
| dannocummed |
| nsin |
| 7 |
18-22 23-26 27-30 44-51 52-60 61- 31-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 9 |
prov10-12 prov11 prov2-9 prov4 prov5 prov6 prov7 prov8 prov1-3 |
| 2231 |
5247.0680 |
2.3519 |
| 2231 |
2607.1966 |
1.1686 |
| 2231 |
14042.0724 |
6.2941 |
| 2231 |
6977.3144 |
3.1274 |
| |
-20173.9912 |
|
| |
-20173.9912 |
|
| |
40385.9824 |
|
| |
40386.3234 |
|
| |
40494.6290 |
|
| |
1 |
7.8570 |
0.0567 |
7.7458 |
7.9682 |
19185.3 |
<.0001 |
| 18-22 |
1 |
0.2319 |
0.0502 |
0.1335 |
0.3302 |
21.35 |
<.0001 |
| 23-26 |
1 |
0.1630 |
0.0444 |
0.0760 |
0.2500 |
13.49 |
0.0002 |
| 27-30 |
1 |
0.1060 |
0.0462 |
0.0154 |
0.1967 |
5.26 |
0.0218 |
| 44-51 |
1 |
-0.1213 |
0.0400 |
-0.1996 |
-0.0429 |
9.20 |
0.0024 |
| 52-60 |
1 |
-0.0216 |
0.0413 |
-0.1025 |
0.0592 |
0.28 |
0.5999 |
| 61- |
1 |
-0.0662 |
0.0443 |
-0.1530 |
0.0207 |
2.23 |
0.1355 |
| 31-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.2019 |
0.0271 |
-0.2550 |
-0.1489 |
55.61 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
0.1309 |
0.0410 |
0.0505 |
0.2113 |
10.19 |
0.0014 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
0.1143 |
0.0308 |
0.0538 |
0.1747 |
13.73 |
0.0002 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10-12 |
1 |
0.2506 |
0.0624 |
0.1282 |
0.3729 |
16.11 |
<.0001 |
| prov11 |
1 |
-0.2226 |
0.0653 |
-0.3505 |
-0.0947 |
11.63 |
0.0006 |
| prov2-9 |
1 |
-0.1788 |
0.0555 |
-0.2877 |
-0.0700 |
10.36 |
0.0013 |
| prov4 |
1 |
0.1136 |
0.0438 |
0.0277 |
0.1994 |
6.72 |
0.0095 |
| prov5 |
1 |
0.1024 |
0.0436 |
0.0170 |
0.1878 |
5.53 |
0.0187 |
| prov6 |
1 |
0.2153 |
0.0460 |
0.1252 |
0.3055 |
21.92 |
<.0001 |
| prov7 |
1 |
0.0076 |
0.0576 |
-0.1053 |
0.1206 |
0.02 |
0.8947 |
| prov8 |
1 |
-0.0222 |
0.0401 |
-0.1008 |
0.0564 |
0.31 |
0.5797 |
| prov1-3 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
1 |
0.4969 |
0.0131 |
0.4719 |
0.5232 |
|
|
Note:The scale parameter was estimated by maximum likelihood.
| 6 |
72.63 |
<.0001 |
| 1 |
56.11 |
<.0001 |
| 1 |
9.85 |
0.0017 |
| 1 |
13.44 |
0.0002 |
| 8 |
82.57 |
<.0001 |
ods select contrasts;
proc genmod data = dannicum;
class eta(ref='31-43') potkil bendie capoluogo prov(ref='prov1-3');
model dannocummed = eta potkil bendie capoluogo prov /
dist = gamma
link = log
type3;
weight nsin;
contrast "eta" eta 1 -1 0 0 0 0 0,
eta 0 0 1 0 0 0 -1,
eta 0 0 0 1 -1 0 0,
eta 0 0 0 0 1 -1 0;
run;
SAS Output
proc format;
value classeta
low-26 = "18-26"
27-43 = "27-43"
44-high = "44-";
run;
proc print data = polizze (obs = 10);
run;
SAS Output
| F |
27-43 |
prov8 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
27-43 |
prov5 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44- |
prov7 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
18-26 |
prov10-12 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44- |
prov2-9 |
NO |
B |
-57 |
-1030 |
8-13 |
0.20000 |
0 |
0.000 |
0 |
-1.60944 |
| F |
44- |
prov8 |
NO |
B |
-57 |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
27-43 |
prov1-3 |
NO |
D |
-57 |
1031-1379 |
17-21 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44- |
prov1-3 |
SI |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
44- |
prov1-3 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44- |
prov1-3 |
NO |
B |
58- |
1031-1379 |
17-21 |
1.00000 |
1 |
359.057 |
1 |
0.00000 |
proc genmod data = dannicum;
class eta(ref='27-43') potkil bendie capoluogo prov(ref='prov1-3');
model dannocummed = eta potkil bendie capoluogo prov /
dist = gamma
link = log
type3;
weight nsin;
run;
SAS Output
| WORK.DANNICUM |
| Gamma |
| Log |
| dannocummed |
| nsin |
| 3 |
18-26 44- 27-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 9 |
prov10-12 prov11 prov2-9 prov4 prov5 prov6 prov7 prov8 prov1-3 |
| 2235 |
5270.5175 |
2.3582 |
| 2235 |
2608.3318 |
1.1670 |
| 2235 |
14183.7232 |
6.3462 |
| 2235 |
7019.3974 |
3.1407 |
| |
-20179.8054 |
|
| |
-20179.8054 |
|
| |
40389.6107 |
|
| |
40389.8257 |
|
| |
40475.3844 |
|
| |
1 |
7.8888 |
0.0554 |
7.7803 |
7.9973 |
20292.3 |
<.0001 |
| 18-26 |
1 |
0.1602 |
0.0351 |
0.0915 |
0.2290 |
20.87 |
<.0001 |
| 44- |
1 |
-0.1030 |
0.0286 |
-0.1589 |
-0.0470 |
13.00 |
0.0003 |
| 27-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.2030 |
0.0269 |
-0.2558 |
-0.1502 |
56.84 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
0.1303 |
0.0411 |
0.0498 |
0.2109 |
10.06 |
0.0015 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
0.1183 |
0.0308 |
0.0579 |
0.1787 |
14.72 |
0.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov10-12 |
1 |
0.2544 |
0.0625 |
0.1320 |
0.3769 |
16.58 |
<.0001 |
| prov11 |
1 |
-0.2284 |
0.0653 |
-0.3564 |
-0.1004 |
12.23 |
0.0005 |
| prov2-9 |
1 |
-0.1774 |
0.0555 |
-0.2862 |
-0.0685 |
10.20 |
0.0014 |
| prov4 |
1 |
0.1049 |
0.0438 |
0.0190 |
0.1907 |
5.73 |
0.0167 |
| prov5 |
1 |
0.0992 |
0.0435 |
0.0139 |
0.1844 |
5.20 |
0.0226 |
| prov6 |
1 |
0.2181 |
0.0459 |
0.1281 |
0.3082 |
22.55 |
<.0001 |
| prov7 |
1 |
0.0079 |
0.0577 |
-0.1051 |
0.1210 |
0.02 |
0.8907 |
| prov8 |
1 |
-0.0251 |
0.0400 |
-0.1035 |
0.0533 |
0.39 |
0.5303 |
| prov1-3 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
1 |
0.4949 |
0.0130 |
0.4700 |
0.5211 |
|
|
Note:The scale parameter was estimated by maximum likelihood.
| 2 |
61.00 |
<.0001 |
| 1 |
57.39 |
<.0001 |
| 1 |
9.73 |
0.0018 |
| 1 |
14.40 |
0.0001 |
| 8 |
83.49 |
<.0001 |
ods select contrasts;
proc genmod data = dannicum;
class eta(ref='27-43') potkil bendie capoluogo prov(ref='prov1-3');
model dannocummed = eta potkil bendie capoluogo prov /
dist = gamma
link = log;
weight nsin;
contrasts "province" prov 0 0 0 0 0 0 1 0 -1,
prov 0 0 0 0 0 0 0 1 -1,
prov 0 0 0 1 -1 0 0 0 0,
prov 1 0 0 0 0 -1 0 0 0,
prov 0 1 -1 0 0 0 0 0 0;
run;
SAS Output
proc format;
value $classprov
"RC","VT","CN","OR","RA","VC","FE","LC","SS","VV","BZ","PV","RG","CH","PG","AR","TE","TN","VR","EN","NO","SV","VI","MC","MT","RE","BS","RI","AG","AV","PC","LE","RN","AN","MS","BO","GE","TS","CB","FI","NU","PE","TO","MI" = "prov1-3-7-8"
"BN","PO","IM","BA","PT","TA","SP","CA","ROMA","PA","AO","NA","CE","KR" = "prov2-9-11"
"AL","SO","GO","LT","PR","PN","GR","UD","TV","PD","SI","TR","AP","LO","FG","ME","LU","CZ","FR","CT","VE","BG","IS","MO","TP" = "prov4-5"
"CL","PI","VA","BR","FO","LI","SR","CO","SA","BL","PZ","BI","CR","CS","AT","MN","PS","AQ","RSM","VB","RO" = "prov6-10-12"
run;
proc print data = polizze (obs = 10);
run;
SAS Output
| F |
27-43 |
prov1-3-7-8 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
27-43 |
prov4-5 |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44- |
prov1-3-7-8 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
18-26 |
prov6-10-12 run |
NO |
B |
-57 |
-1030 |
8-13 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44- |
prov2-9-11 |
NO |
B |
-57 |
-1030 |
8-13 |
0.20000 |
0 |
0.000 |
0 |
-1.60944 |
| F |
44- |
prov1-3-7-8 |
NO |
B |
-57 |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
27-43 |
prov1-3-7-8 |
NO |
D |
-57 |
1031-1379 |
17-21 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44- |
prov1-3-7-8 |
SI |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| F |
44- |
prov1-3-7-8 |
NO |
B |
58- |
-1030 |
14-15 |
1.00000 |
0 |
0.000 |
0 |
0.00000 |
| M |
44- |
prov1-3-7-8 |
NO |
B |
58- |
1031-1379 |
17-21 |
1.00000 |
1 |
359.057 |
1 |
0.00000 |
proc genmod data = dannicum plots = stdreschi(xbeta);
class eta(ref='27-43') potkil bendie capoluogo prov(ref='prov1-3-7-8');
model dannocummed = eta potkil bendie capoluogo prov /
dist = gamma
link = log
type3;
weight nsin;
run;
SAS Output
| WORK.DANNICUM |
| Gamma |
| Log |
| dannocummed |
| nsin |
| 3 |
18-26 44- 27-43 |
| 2 |
-57 58- |
| 2 |
B D |
| 2 |
NO SI |
| 4 |
prov2-9-11 prov4-5 prov6-10-12 run prov1-3-7-8 |
| 2240 |
5272.9949 |
2.3540 |
| 2240 |
2608.4516 |
1.1645 |
| 2240 |
14116.3074 |
6.3019 |
| 2240 |
6983.0724 |
3.1174 |
| |
-20180.4183 |
|
| |
-20180.4183 |
|
| |
40380.8365 |
|
| |
40380.9348 |
|
| |
40438.0189 |
|
| |
1 |
7.8775 |
0.0518 |
7.7760 |
7.9790 |
23119.8 |
<.0001 |
| 18-26 |
1 |
0.1592 |
0.0351 |
0.0905 |
0.2279 |
20.61 |
<.0001 |
| 44- |
1 |
-0.1031 |
0.0285 |
-0.1590 |
-0.0472 |
13.07 |
0.0003 |
| 27-43 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| -57 |
1 |
-0.2028 |
0.0269 |
-0.2555 |
-0.1500 |
56.78 |
<.0001 |
| 58- |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| B |
1 |
0.1324 |
0.0409 |
0.0522 |
0.2125 |
10.46 |
0.0012 |
| D |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| NO |
1 |
0.1209 |
0.0305 |
0.0610 |
0.1807 |
15.65 |
<.0001 |
| SI |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| prov2-9-11 |
1 |
-0.1897 |
0.0425 |
-0.2729 |
-0.1064 |
19.92 |
<.0001 |
| prov4-5 |
1 |
0.1095 |
0.0312 |
0.0484 |
0.1707 |
12.33 |
0.0004 |
| prov6-10-12 run |
1 |
0.2369 |
0.0369 |
0.1645 |
0.3093 |
41.12 |
<.0001 |
| prov1-3-7-8 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
1 |
0.4947 |
0.0130 |
0.4698 |
0.5209 |
|
|
Note:The scale parameter was estimated by maximum likelihood.
| 2 |
60.76 |
<.0001 |
| 1 |
57.34 |
<.0001 |
| 1 |
10.11 |
0.0015 |
| 1 |
15.29 |
<.0001 |
| 3 |
82.27 |
<.0001 |
4) Riservazione con i GLM
Preparazione dei dati
data runoff;
set dati.runoff;
run;
proc print data = runoff (obs = 10);
run;
SAS Output
| 10775462 |
32165 |
0 |
0 |
0 |
| 9159050 |
32165 |
0 |
1 |
1 |
| 2581795 |
32165 |
0 |
2 |
2 |
| 1380284 |
32165 |
0 |
3 |
3 |
| 871723 |
32165 |
0 |
4 |
4 |
| 589888 |
32165 |
0 |
5 |
5 |
| 1275556 |
32165 |
0 |
6 |
6 |
| 1643537 |
32165 |
0 |
7 |
7 |
| 522288 |
32165 |
0 |
8 |
8 |
| 645271 |
32165 |
0 |
9 |
9 |
data runoff1;
set runoff;
pagamentinden = pagamenti / nden;
logpagamenti = log(pagamenti);
run;
proc print data = runoff1 (obs = 10);
run;
SAS Output
| 10775462 |
32165 |
0 |
0 |
0 |
335.006 |
16.1928 |
| 9159050 |
32165 |
0 |
1 |
1 |
284.752 |
16.0303 |
| 2581795 |
32165 |
0 |
2 |
2 |
80.267 |
14.7640 |
| 1380284 |
32165 |
0 |
3 |
3 |
42.913 |
14.1378 |
| 871723 |
32165 |
0 |
4 |
4 |
27.102 |
13.6782 |
| 589888 |
32165 |
0 |
5 |
5 |
18.339 |
13.2877 |
| 1275556 |
32165 |
0 |
6 |
6 |
39.657 |
14.0589 |
| 1643537 |
32165 |
0 |
7 |
7 |
51.097 |
14.3124 |
| 522288 |
32165 |
0 |
8 |
8 |
16.238 |
13.1660 |
| 645271 |
32165 |
0 |
9 |
9 |
20.061 |
13.3774 |
Modello Poisson-Logaritmo
- Variabili risposta: $Y_i = P_{ij}$ (
pagamenti), con distribuzione di Poisson;
- Variabili esplicative: $i$ (
annoacc) e $j$ (annodiff), di classificazione $\eta_{ij}=\boldsymbol{x}'\beta = \mu + \alpha_i + \beta_j$ ;
- Funzione di collegamento: $g=log$.
proc genmod data = runoff1;
class annoacc (ref = first) annodiff (ref = first);
model pagamenti = annoacc annodiff /
dist = poisson
link = log
type3;
run;
SAS Output
| WORK.RUNOFF1 |
|
| Poisson |
|
| Log |
|
| pagamenti |
pagamenti |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 78 |
14260424.598 |
182825.9564 |
| 78 |
14260424.598 |
182825.9564 |
| 78 |
14447110.935 |
185219.3710 |
| 78 |
14447110.935 |
185219.3710 |
| |
9218270255.4 |
|
| |
-7131082.019 |
|
| |
14262218.039 |
|
| |
14262237.675 |
|
| |
14262289.696 |
|
| |
1 |
16.1578 |
0.0002 |
16.1574 |
16.1581 |
7.225E9 |
<.0001 |
| 1 |
1 |
0.1685 |
0.0002 |
0.1681 |
0.1690 |
473998 |
<.0001 |
| 2 |
1 |
0.3099 |
0.0002 |
0.3095 |
0.3104 |
1688300 |
<.0001 |
| 3 |
1 |
0.1911 |
0.0002 |
0.1906 |
0.1916 |
605889 |
<.0001 |
| 4 |
1 |
0.2646 |
0.0002 |
0.2641 |
0.2650 |
1191696 |
<.0001 |
| 5 |
1 |
0.4359 |
0.0002 |
0.4354 |
0.4364 |
3451576 |
<.0001 |
| 6 |
1 |
0.5303 |
0.0002 |
0.5299 |
0.5308 |
5257320 |
<.0001 |
| 7 |
1 |
0.5360 |
0.0002 |
0.5355 |
0.5364 |
5290452 |
<.0001 |
| 8 |
1 |
0.6910 |
0.0002 |
0.6906 |
0.6915 |
9217844 |
<.0001 |
| 9 |
1 |
0.7318 |
0.0002 |
0.7314 |
0.7323 |
1.034E7 |
<.0001 |
| 10 |
1 |
0.8491 |
0.0002 |
0.8487 |
0.8496 |
1.427E7 |
<.0001 |
| 11 |
1 |
0.7718 |
0.0002 |
0.7713 |
0.7722 |
1.114E7 |
<.0001 |
| 12 |
1 |
0.7203 |
0.0002 |
0.7198 |
0.7207 |
8877816 |
<.0001 |
| 13 |
1 |
0.7465 |
0.0003 |
0.7460 |
0.7471 |
6821783 |
<.0001 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1 |
1 |
-0.0887 |
0.0001 |
-0.0889 |
-0.0886 |
847441 |
<.0001 |
| 2 |
1 |
-1.1171 |
0.0001 |
-1.1173 |
-1.1168 |
6.342E7 |
<.0001 |
| 3 |
1 |
-1.7941 |
0.0002 |
-1.7945 |
-1.7937 |
8.443E7 |
<.0001 |
| 4 |
1 |
-2.3215 |
0.0003 |
-2.3220 |
-2.3209 |
7.675E7 |
<.0001 |
| 5 |
1 |
-2.3994 |
0.0003 |
-2.4000 |
-2.3988 |
6.61E7 |
<.0001 |
| 6 |
1 |
-2.7240 |
0.0004 |
-2.7247 |
-2.7232 |
5.33E7 |
<.0001 |
| 7 |
1 |
-2.2936 |
0.0003 |
-2.2942 |
-2.2929 |
4.818E7 |
<.0001 |
| 8 |
1 |
-3.0068 |
0.0005 |
-3.0078 |
-3.0058 |
3.435E7 |
<.0001 |
| 9 |
1 |
-3.2233 |
0.0006 |
-3.2246 |
-3.2221 |
2.552E7 |
<.0001 |
| 10 |
1 |
-3.3294 |
0.0008 |
-3.3309 |
-3.3279 |
1.93E7 |
<.0001 |
| 11 |
1 |
-3.6627 |
0.0010 |
-3.6647 |
-3.6607 |
1.255E7 |
<.0001 |
| 12 |
1 |
-3.1271 |
0.0010 |
-3.1291 |
-3.1251 |
9564465 |
<.0001 |
| 13 |
1 |
-2.3422 |
0.0010 |
-2.3442 |
-2.3402 |
5294849 |
<.0001 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
1.0000 |
0.0000 |
1.0000 |
1.0000 |
|
|
Note:The scale parameter was held fixed.
| 13 |
3.667E7 |
<.0001 |
| 13 |
4.948E8 |
<.0001 |
Modello Gamma-Logaritmo
- Variabili risposta: $Y_i = P_{ij}$ (
pagamenti), con distribuzione gamma;
- Variabili esplicative: $i$ (
annoacc) e $j$ (annodiff), di classificazione $\eta_{ij}=\boldsymbol{x}'\beta = \mu + \alpha_i + \beta_j$ ;
- Funzione di collegamento: $g=log$.
proc genmod data = runoff1;
class annoacc (ref = first) annodiff (ref = first);
model pagamenti = annoacc annodiff /
dist = gamma
link = log
scale = pearson
type3;
run;
SAS Output
| WORK.RUNOFF1 |
|
| Gamma |
|
| Log |
|
| pagamenti |
pagamenti |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 78 |
9.9323 |
0.1273 |
| 78 |
88.4751 |
1.1343 |
| 78 |
8.7563 |
0.1123 |
| 78 |
78.0000 |
1.0000 |
| |
-1573.3582 |
|
| |
-1573.3582 |
|
| |
3200.7164 |
|
| |
3220.3528 |
|
| |
3272.3733 |
|
| |
1 |
16.3646 |
0.1400 |
16.0903 |
16.6390 |
13666.4 |
<.0001 |
| 1 |
1 |
0.2396 |
0.1320 |
-0.0191 |
0.4983 |
3.29 |
0.0695 |
| 2 |
1 |
0.2364 |
0.1377 |
-0.0334 |
0.5062 |
2.95 |
0.0859 |
| 3 |
1 |
-0.0378 |
0.1415 |
-0.3151 |
0.2395 |
0.07 |
0.7893 |
| 4 |
1 |
-0.0195 |
0.1477 |
-0.3091 |
0.2700 |
0.02 |
0.8947 |
| 5 |
1 |
0.1012 |
0.1534 |
-0.1995 |
0.4020 |
0.44 |
0.5095 |
| 6 |
1 |
0.1889 |
0.1590 |
-0.1227 |
0.5005 |
1.41 |
0.2348 |
| 7 |
1 |
0.3370 |
0.1657 |
0.0122 |
0.6617 |
4.14 |
0.0420 |
| 8 |
1 |
0.4124 |
0.1759 |
0.0677 |
0.7572 |
5.50 |
0.0190 |
| 9 |
1 |
0.4317 |
0.1873 |
0.0646 |
0.7988 |
5.31 |
0.0212 |
| 10 |
1 |
0.6940 |
0.2032 |
0.2959 |
1.0922 |
11.67 |
0.0006 |
| 11 |
1 |
0.6255 |
0.2270 |
0.1806 |
1.0704 |
7.59 |
0.0059 |
| 12 |
1 |
0.5253 |
0.2675 |
0.0009 |
1.0496 |
3.85 |
0.0496 |
| 13 |
1 |
0.5396 |
0.3631 |
-0.1721 |
1.2513 |
2.21 |
0.1372 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1 |
1 |
-0.1047 |
0.1315 |
-0.3625 |
0.1530 |
0.63 |
0.4258 |
| 2 |
1 |
-1.1463 |
0.1355 |
-1.4119 |
-0.8808 |
71.57 |
<.0001 |
| 3 |
1 |
-1.7918 |
0.1395 |
-2.0653 |
-1.5183 |
164.87 |
<.0001 |
| 4 |
1 |
-2.2928 |
0.1438 |
-2.5747 |
-2.0109 |
254.07 |
<.0001 |
| 5 |
1 |
-2.4195 |
0.1498 |
-2.7131 |
-2.1259 |
260.93 |
<.0001 |
| 6 |
1 |
-2.7622 |
0.1560 |
-3.0679 |
-2.4564 |
313.52 |
<.0001 |
| 7 |
1 |
-2.3163 |
0.1632 |
-2.6362 |
-1.9965 |
201.46 |
<.0001 |
| 8 |
1 |
-3.0787 |
0.1727 |
-3.4171 |
-2.7403 |
317.93 |
<.0001 |
| 9 |
1 |
-3.3611 |
0.1859 |
-3.7255 |
-2.9966 |
326.74 |
<.0001 |
| 10 |
1 |
-3.4670 |
0.2027 |
-3.8644 |
-3.0697 |
292.44 |
<.0001 |
| 11 |
1 |
-3.8490 |
0.2256 |
-4.2911 |
-3.4069 |
291.13 |
<.0001 |
| 12 |
1 |
-3.3855 |
0.2673 |
-3.9093 |
-2.8616 |
160.41 |
<.0001 |
| 13 |
1 |
-2.5491 |
0.3631 |
-3.2608 |
-1.8374 |
49.28 |
<.0001 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
8.9078 |
0.0000 |
8.9078 |
8.9078 |
|
|
Note:The Gamma scale parameter was estimated by DOF/Pearson's Chi-Square
| 13 |
78 |
2.52 |
0.0061 |
32.80 |
0.0018 |
| 13 |
78 |
84.19 |
<.0001 |
1094.46 |
<.0001 |
Modello di Poisson con Sovradispersione-Logaritmo
- Variabili risposta: $Y_i = P_{ij}$ (
pagamenti), Poisson con Sovradispersione;
- Variabili esplicative: $i$ (
annoacc) e $j$ (annodiff), di classificazione $\eta_{ij}=\boldsymbol{x}'\beta = \mu + \alpha_i + \beta_j$ ;
- Funzione di collegamento: $g=log$.
proc genmod data = runoff1;
class annoacc (ref = first) annodiff (ref = first);
model pagamenti = annoacc annodiff /
dist = poisson
link = log
scale = pearson
type3;
run;
SAS Output
| WORK.RUNOFF1 |
|
| Poisson |
|
| Log |
|
| pagamenti |
pagamenti |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 78 |
14260424.598 |
182825.9564 |
| 78 |
76.9921 |
0.9871 |
| 78 |
14447110.935 |
185219.3710 |
| 78 |
78.0000 |
1.0000 |
| |
49769.4718 |
|
| |
-7131082.019 |
|
| |
14262218.039 |
|
| |
14262237.675 |
|
| |
14262289.696 |
|
| |
1 |
16.1578 |
0.0818 |
15.9974 |
16.3181 |
39008.2 |
<.0001 |
| 1 |
1 |
0.1685 |
0.1054 |
-0.0380 |
0.3750 |
2.56 |
0.1097 |
| 2 |
1 |
0.3099 |
0.1027 |
0.1087 |
0.5111 |
9.12 |
0.0025 |
| 3 |
1 |
0.1911 |
0.1057 |
-0.0160 |
0.3982 |
3.27 |
0.0705 |
| 4 |
1 |
0.2646 |
0.1043 |
0.0601 |
0.4690 |
6.43 |
0.0112 |
| 5 |
1 |
0.4359 |
0.1010 |
0.2380 |
0.6338 |
18.64 |
<.0001 |
| 6 |
1 |
0.5303 |
0.0995 |
0.3352 |
0.7254 |
28.38 |
<.0001 |
| 7 |
1 |
0.5360 |
0.1003 |
0.3394 |
0.7325 |
28.56 |
<.0001 |
| 8 |
1 |
0.6910 |
0.0980 |
0.4990 |
0.8830 |
49.77 |
<.0001 |
| 9 |
1 |
0.7318 |
0.0980 |
0.5398 |
0.9238 |
55.81 |
<.0001 |
| 10 |
1 |
0.8491 |
0.0968 |
0.6595 |
1.0387 |
77.02 |
<.0001 |
| 11 |
1 |
0.7718 |
0.0995 |
0.5767 |
0.9668 |
60.16 |
<.0001 |
| 12 |
1 |
0.7203 |
0.1040 |
0.5164 |
0.9242 |
47.93 |
<.0001 |
| 13 |
1 |
0.7465 |
0.1230 |
0.5054 |
0.9876 |
36.83 |
<.0001 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1 |
1 |
-0.0887 |
0.0415 |
-0.1701 |
-0.0074 |
4.58 |
0.0324 |
| 2 |
1 |
-1.1171 |
0.0604 |
-1.2354 |
-0.9987 |
342.42 |
<.0001 |
| 3 |
1 |
-1.7941 |
0.0840 |
-1.9588 |
-1.6294 |
455.86 |
<.0001 |
| 4 |
1 |
-2.3215 |
0.1140 |
-2.5450 |
-2.0979 |
414.38 |
<.0001 |
| 5 |
1 |
-2.3994 |
0.1270 |
-2.6484 |
-2.1505 |
356.89 |
<.0001 |
| 6 |
1 |
-2.7240 |
0.1606 |
-3.0387 |
-2.4093 |
287.77 |
<.0001 |
| 7 |
1 |
-2.2936 |
0.1422 |
-2.5723 |
-2.0149 |
260.13 |
<.0001 |
| 8 |
1 |
-3.0068 |
0.2208 |
-3.4396 |
-2.5741 |
185.47 |
<.0001 |
| 9 |
1 |
-3.2233 |
0.2746 |
-3.7615 |
-2.6852 |
137.81 |
<.0001 |
| 10 |
1 |
-3.3294 |
0.3262 |
-3.9687 |
-2.6901 |
104.19 |
<.0001 |
| 11 |
1 |
-3.6627 |
0.4449 |
-4.5347 |
-2.7907 |
67.78 |
<.0001 |
| 12 |
1 |
-3.1271 |
0.4352 |
-3.9800 |
-2.2742 |
51.64 |
<.0001 |
| 13 |
1 |
-2.3422 |
0.4381 |
-3.2008 |
-1.4836 |
28.59 |
<.0001 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
430.3712 |
0.0000 |
430.3712 |
430.3712 |
|
|
Note:The scale parameter was estimated by the square root of Pearson's Chi-Square/DOF.
| 13 |
78 |
15.23 |
<.0001 |
198.00 |
<.0001 |
| 13 |
78 |
205.48 |
<.0001 |
2671.22 |
<.0001 |
Modello di Poisson con Sovradispersione-Logaritmo per pagamenti rapportati a una misura di esposizione
- Variabili risposta: $Y_{ij} = \frac{P_{ij}}{w_{i}}$ pagamenti rapportati al numero di sinistri dell'anno $i$ denunciati nell’anno di accadimento $w_i$, Poisson con Sovradispersione, con pesi i numeri di sinistri dell'anno $i$ denunciati nell’anno di accadimento $\omega_i = w_i$;
- Variabili esplicative: $i$ (
annoacc) e $j$ (annodiff), di classificazione $\eta_{ij}=\boldsymbol{x}'\beta = \mu + \alpha_i + \beta_j$ ;
- Funzione di collegamento: $g=log$.
proc genmod data = runoff1;
class annoacc (ref = first) annodiff (ref = first);
model pagamentinden = annoacc annodiff /
dist = poisson
link = log
scale = pearson
type3;
weight nden;
run;
SAS Output
| WORK.RUNOFF1 |
|
| Poisson |
|
| Log |
|
| pagamentinden |
|
| nden |
nden |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 78 |
14260424.598 |
182825.9564 |
| 78 |
76.9921 |
0.9871 |
| 78 |
14447110.935 |
185219.3710 |
| 78 |
78.0000 |
1.0000 |
| |
16546.6067 |
|
| |
-16497154.04 |
|
| |
32994362.072 |
|
| |
32994381.708 |
|
| |
32994433.729 |
|
| |
1 |
5.7791 |
0.0818 |
5.6188 |
5.9395 |
4990.20 |
<.0001 |
| 1 |
1 |
0.1776 |
0.1054 |
-0.0289 |
0.3841 |
2.84 |
0.0919 |
| 2 |
1 |
0.3268 |
0.1027 |
0.1256 |
0.5280 |
10.14 |
0.0015 |
| 3 |
1 |
0.2943 |
0.1057 |
0.0872 |
0.5014 |
7.76 |
0.0053 |
| 4 |
1 |
0.3942 |
0.1043 |
0.1897 |
0.5986 |
14.28 |
0.0002 |
| 5 |
1 |
0.5141 |
0.1010 |
0.3162 |
0.7120 |
25.92 |
<.0001 |
| 6 |
1 |
0.5967 |
0.0995 |
0.4016 |
0.7918 |
35.94 |
<.0001 |
| 7 |
1 |
0.6257 |
0.1003 |
0.4292 |
0.8223 |
38.93 |
<.0001 |
| 8 |
1 |
1.0454 |
0.0980 |
0.8534 |
1.2374 |
113.90 |
<.0001 |
| 9 |
1 |
1.0019 |
0.0980 |
0.8099 |
1.1939 |
104.60 |
<.0001 |
| 10 |
1 |
1.2260 |
0.0968 |
1.0364 |
1.4156 |
160.57 |
<.0001 |
| 11 |
1 |
1.2347 |
0.0995 |
1.0397 |
1.4297 |
153.98 |
<.0001 |
| 12 |
1 |
1.3203 |
0.1040 |
1.1164 |
1.5242 |
161.06 |
<.0001 |
| 13 |
1 |
1.3778 |
0.1230 |
1.1368 |
1.6189 |
125.47 |
<.0001 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1 |
1 |
-0.0887 |
0.0415 |
-0.1701 |
-0.0074 |
4.58 |
0.0324 |
| 2 |
1 |
-1.1171 |
0.0604 |
-1.2354 |
-0.9987 |
342.42 |
<.0001 |
| 3 |
1 |
-1.7941 |
0.0840 |
-1.9588 |
-1.6294 |
455.86 |
<.0001 |
| 4 |
1 |
-2.3215 |
0.1140 |
-2.5450 |
-2.0979 |
414.38 |
<.0001 |
| 5 |
1 |
-2.3994 |
0.1270 |
-2.6484 |
-2.1505 |
356.89 |
<.0001 |
| 6 |
1 |
-2.7240 |
0.1606 |
-3.0387 |
-2.4093 |
287.77 |
<.0001 |
| 7 |
1 |
-2.2936 |
0.1422 |
-2.5723 |
-2.0149 |
260.13 |
<.0001 |
| 8 |
1 |
-3.0068 |
0.2208 |
-3.4396 |
-2.5741 |
185.47 |
<.0001 |
| 9 |
1 |
-3.2233 |
0.2746 |
-3.7615 |
-2.6852 |
137.81 |
<.0001 |
| 10 |
1 |
-3.3294 |
0.3262 |
-3.9687 |
-2.6901 |
104.19 |
<.0001 |
| 11 |
1 |
-3.6627 |
0.4449 |
-4.5347 |
-2.7907 |
67.78 |
<.0001 |
| 12 |
1 |
-3.1271 |
0.4352 |
-3.9800 |
-2.2742 |
51.64 |
<.0001 |
| 13 |
1 |
-2.3422 |
0.4381 |
-3.2008 |
-1.4836 |
28.59 |
<.0001 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
430.3712 |
0.0000 |
430.3712 |
430.3712 |
|
|
Note:The scale parameter was estimated by the square root of Pearson's Chi-Square/DOF.
| 13 |
78 |
42.02 |
<.0001 |
546.21 |
<.0001 |
| 13 |
78 |
205.48 |
<.0001 |
2671.22 |
<.0001 |
Modello di Poisson-Composto-Logaritmo per pagamenti rapportati a una misura di esposizione
- Variabili risposta: $Y_{ij} = \frac{P_{ij}}{w_{i}}$ pagamenti rapportati al numero di sinistri dell'anno $i$ denunciati nell’anno di accadimento $w_i$, Poisson-Composta, con pesi i numeri di sinistri dell'anno $i$ denunciati nell’anno di accadimento $\omega_i = w_i$;
- Variabili esplicative: $i$ (
annoacc) e $j$ (annodiff), di classificazione $\eta_{ij}=\boldsymbol{x}'\beta = \mu + \alpha_i + \beta_j$ ;
- Funzione di collegamento: $g=log$.
proc genmod data = runoff1;
class annoacc (ref = first) annodiff (ref = first);
csi = 1.01887;
y = _RESP_;
mu = _MEAN_;
variance var = mu
if y = 0 then
d = 2
else
d = -2
deviance dev = d;
model pagamentinden = annoacc annodiff /
link = log
scale = pearson
type3;
weight nden;
run;
SAS Output
| WORK.RUNOFF1 |
|
| User |
|
| Log |
|
| pagamentinden |
|
| nden |
nden |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 78 |
13163753.882 |
168766.0754 |
| 78 |
72.4134 |
0.9284 |
| 78 |
14179315.033 |
181786.0902 |
| 78 |
78.0000 |
1.0000 |
| |
-36.2067 |
|
| |
-36.2067 |
|
| |
126.4134 |
|
| |
146.0498 |
|
| |
198.0704 |
|
| |
1 |
5.7791 |
0.0818 |
5.6188 |
5.9395 |
4990.30 |
<.0001 |
| 1 |
1 |
0.1776 |
0.1054 |
-0.0289 |
0.3841 |
2.84 |
0.0919 |
| 2 |
1 |
0.3268 |
0.1027 |
0.1256 |
0.5280 |
10.14 |
0.0015 |
| 3 |
1 |
0.2943 |
0.1057 |
0.0872 |
0.5014 |
7.76 |
0.0053 |
| 4 |
1 |
0.3942 |
0.1043 |
0.1897 |
0.5986 |
14.28 |
0.0002 |
| 5 |
1 |
0.5141 |
0.1010 |
0.3162 |
0.7120 |
25.92 |
<.0001 |
| 6 |
1 |
0.5967 |
0.0995 |
0.4016 |
0.7918 |
35.94 |
<.0001 |
| 7 |
1 |
0.6257 |
0.1003 |
0.4292 |
0.8223 |
38.94 |
<.0001 |
| 8 |
1 |
1.0454 |
0.0980 |
0.8534 |
1.2374 |
113.91 |
<.0001 |
| 9 |
1 |
1.0019 |
0.0980 |
0.8099 |
1.1939 |
104.60 |
<.0001 |
| 10 |
1 |
1.2260 |
0.0968 |
1.0364 |
1.4156 |
160.57 |
<.0001 |
| 11 |
1 |
1.2347 |
0.0995 |
1.0397 |
1.4297 |
153.99 |
<.0001 |
| 12 |
1 |
1.3203 |
0.1040 |
1.1164 |
1.5242 |
161.06 |
<.0001 |
| 13 |
1 |
1.3778 |
0.1230 |
1.1368 |
1.6189 |
125.47 |
<.0001 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1 |
1 |
-0.0887 |
0.0415 |
-0.1701 |
-0.0074 |
4.58 |
0.0324 |
| 2 |
1 |
-1.1171 |
0.0604 |
-1.2354 |
-0.9988 |
342.42 |
<.0001 |
| 3 |
1 |
-1.7941 |
0.0840 |
-1.9588 |
-1.6294 |
455.86 |
<.0001 |
| 4 |
1 |
-2.3215 |
0.1140 |
-2.5450 |
-2.0979 |
414.39 |
<.0001 |
| 5 |
1 |
-2.3994 |
0.1270 |
-2.6483 |
-2.1505 |
356.89 |
<.0001 |
| 6 |
1 |
-2.7240 |
0.1606 |
-3.0387 |
-2.4092 |
287.78 |
<.0001 |
| 7 |
1 |
-2.2936 |
0.1422 |
-2.5723 |
-2.0149 |
260.13 |
<.0001 |
| 8 |
1 |
-3.0068 |
0.2208 |
-3.4396 |
-2.5741 |
185.47 |
<.0001 |
| 9 |
1 |
-3.2232 |
0.2746 |
-3.7614 |
-2.6851 |
137.81 |
<.0001 |
| 10 |
1 |
-3.3292 |
0.3261 |
-3.9684 |
-2.6900 |
104.20 |
<.0001 |
| 11 |
1 |
-3.6627 |
0.4449 |
-4.5347 |
-2.7907 |
67.78 |
<.0001 |
| 12 |
1 |
-3.1271 |
0.4352 |
-3.9800 |
-2.2742 |
51.64 |
<.0001 |
| 13 |
1 |
-2.3422 |
0.4381 |
-3.2008 |
-1.4836 |
28.59 |
<.0001 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
426.3638 |
0.0000 |
426.3638 |
426.3638 |
|
|
Note:The scale parameter was estimated by the square root of Pearson's Chi-Square/DOF.
| 13 |
78 |
38.02 |
<.0001 |
494.31 |
<.0001 |
| 13 |
78 |
189.80 |
<.0001 |
2467.38 |
<.0001 |
Modello di Poisson con Sovradispersione-Logaritmo per pagamenti rapportati a una misura di esposizione
- Variabili risposta: $Y_{ij} = \frac{P_{ij}}{w_{i}}$ pagamenti rapportati al numero di sinistri dell'anno $i$ denunciati nell’anno di accadimento $w_i$, Poisson con Sovradispersione, con pesi i numeri di sinistri dell'anno $i$ denunciati nell’anno di accadimento $\omega_i = w_i$;
- Variabili esplicative: $i$ (
annoacc), $j$ (annodiff) e $i+j$ (annopag), di classificazione $\eta_{ij}=\boldsymbol{x}'\beta = \mu + \alpha_i + \beta_j + \gamma_{i+j}$ ;
- Funzione di collegamento: $g=log$.
proc genmod data = runoff1;
class annoacc (ref = first) annodiff (ref = first) annopag;
model pagamentinden = annoacc annodiff annopag /
dist = poisson
link = log
scale = pearson
type3;
weight nden;
run;
SAS Output
| WORK.RUNOFF1 |
|
| Poisson |
|
| Log |
|
| pagamentinden |
|
| nden |
nden |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 14 |
1 2 3 4 5 6 7 8 9 10 11 12 13 0 |
| 14 |
0 1 2 3 4 5 6 7 8 9 10 11 12 13 |
| 66 |
10720784.463 |
162436.1282 |
| 66 |
66.3551 |
1.0054 |
| 66 |
10663412.571 |
161566.8571 |
| 66 |
66.0000 |
1.0000 |
| |
18979.8945 |
|
| |
-14727333.97 |
|
| |
29454745.937 |
|
| |
29454793.937 |
|
| |
29454849.442 |
|
| |
1 |
4.8454 |
1.0388 |
2.8094 |
6.8815 |
21.76 |
<.0001 |
| 1 |
1 |
0.2951 |
0.1395 |
0.0218 |
0.5685 |
4.48 |
0.0343 |
| 2 |
1 |
0.5029 |
0.2050 |
0.1010 |
0.9048 |
6.02 |
0.0142 |
| 3 |
1 |
0.4727 |
0.2792 |
-0.0746 |
1.0200 |
2.87 |
0.0905 |
| 4 |
1 |
0.5844 |
0.3562 |
-0.1137 |
1.2825 |
2.69 |
0.1009 |
| 5 |
1 |
0.7189 |
0.4352 |
-0.1340 |
1.5718 |
2.73 |
0.0985 |
| 6 |
1 |
0.8375 |
0.5145 |
-0.1708 |
1.8459 |
2.65 |
0.1035 |
| 7 |
1 |
0.9726 |
0.5971 |
-0.1978 |
2.1430 |
2.65 |
0.1034 |
| 8 |
1 |
1.5515 |
0.6794 |
0.2199 |
2.8831 |
5.21 |
0.0224 |
| 9 |
1 |
1.6365 |
0.7632 |
0.1407 |
3.1324 |
4.60 |
0.0320 |
| 10 |
1 |
1.9659 |
0.8471 |
0.3057 |
3.6261 |
5.39 |
0.0203 |
| 11 |
1 |
2.0614 |
0.9338 |
0.2312 |
3.8916 |
4.87 |
0.0273 |
| 12 |
1 |
2.2159 |
1.0013 |
0.2534 |
4.1785 |
4.90 |
0.0269 |
| 13 |
1 |
2.3115 |
1.0424 |
0.2686 |
4.3545 |
4.92 |
0.0266 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 1 |
1 |
-0.0107 |
0.0883 |
-0.1837 |
0.1623 |
0.01 |
0.9035 |
| 2 |
1 |
-0.9643 |
0.1713 |
-1.3001 |
-0.6285 |
31.68 |
<.0001 |
| 3 |
1 |
-1.5729 |
0.2573 |
-2.0773 |
-1.0686 |
37.36 |
<.0001 |
| 4 |
1 |
-2.0294 |
0.3463 |
-2.7082 |
-1.3507 |
34.34 |
<.0001 |
| 5 |
1 |
-2.0365 |
0.4297 |
-2.8788 |
-1.1943 |
22.46 |
<.0001 |
| 6 |
1 |
-2.2839 |
0.5202 |
-3.3035 |
-1.2643 |
19.28 |
<.0001 |
| 7 |
1 |
-1.7727 |
0.5968 |
-2.9425 |
-0.6029 |
8.82 |
0.0030 |
| 8 |
1 |
-2.4041 |
0.6964 |
-3.7690 |
-1.0392 |
11.92 |
0.0006 |
| 9 |
1 |
-2.5525 |
0.7921 |
-4.1050 |
-1.0000 |
10.38 |
0.0013 |
| 10 |
1 |
-2.5925 |
0.8877 |
-4.3324 |
-0.8526 |
8.53 |
0.0035 |
| 11 |
1 |
-2.8695 |
1.0014 |
-4.8321 |
-0.9069 |
8.21 |
0.0042 |
| 12 |
1 |
-2.2588 |
1.0688 |
-4.3536 |
-0.1640 |
4.47 |
0.0346 |
| 13 |
1 |
-1.4085 |
1.1139 |
-3.5916 |
0.7746 |
1.60 |
0.2060 |
| 0 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 0 |
1 |
0.9687 |
1.0460 |
-1.0814 |
3.0189 |
0.86 |
0.3544 |
| 1 |
1 |
0.7962 |
0.9600 |
-1.0853 |
2.6777 |
0.69 |
0.4069 |
| 2 |
1 |
0.6252 |
0.8765 |
-1.0927 |
2.3431 |
0.51 |
0.4757 |
| 3 |
1 |
0.6656 |
0.7934 |
-0.8895 |
2.2207 |
0.70 |
0.4016 |
| 4 |
1 |
0.6738 |
0.7101 |
-0.7181 |
2.0656 |
0.90 |
0.3427 |
| 5 |
1 |
0.6838 |
0.6264 |
-0.5439 |
1.9114 |
1.19 |
0.2750 |
| 6 |
1 |
0.7182 |
0.5433 |
-0.3467 |
1.7831 |
1.75 |
0.1862 |
| 7 |
1 |
0.6952 |
0.4604 |
-0.2072 |
1.5976 |
2.28 |
0.1310 |
| 8 |
1 |
0.4907 |
0.3780 |
-0.2501 |
1.2315 |
1.69 |
0.1942 |
| 9 |
1 |
0.3391 |
0.2958 |
-0.2407 |
0.9190 |
1.31 |
0.2516 |
| 10 |
1 |
0.2005 |
0.2142 |
-0.2192 |
0.6203 |
0.88 |
0.3491 |
| 11 |
1 |
0.1177 |
0.1345 |
-0.1460 |
0.3813 |
0.77 |
0.3816 |
| 12 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| 13 |
0 |
0.0000 |
0.0000 |
0.0000 |
0.0000 |
. |
. |
| |
0 |
401.9538 |
0.0000 |
401.9538 |
401.9538 |
|
|
Note:The scale parameter was estimated by the square root of Pearson's Chi-Square/DOF.
| 12 |
66 |
3.79 |
0.0002 |
45.53 |
<.0001 |
| 12 |
66 |
28.48 |
<.0001 |
341.81 |
<.0001 |
| 12 |
66 |
1.83 |
0.0617 |
21.91 |
0.0386 |